How can we make compatible the 'ehipassiko' aspect of the Dhamma with the faith aspects of it?

This question is illogical because the term "ehipassiko" means the Dhamma is not blind faith.

In SN 12.2, "birth" is defined as the mental production the self-view of "beings" based on the manifestation of aggregates experienced via the sense bases. "Re-birth" is the re-arising of these self-views. This is the 'ehipassiko' aspect of Dhamma.

For example, words typed on this internet site are "aggregates" manifesting in different ways. When the mind get annoyed at words read and then produces self-views about the writer and reader of these mere words, such as: "You are a nasty person and you annoy me", this is "birth". Two views of "beings" have been "birthed" from mere words written on an internet page.

Ehipassiko, friends. Come & see, the real verifiable truth (of "re-birth") in the here-&-now.

For example, the suttas do not say the Buddha recollected his "past lives". The Pali word here is "nivasa", which means "abode", "dwelling", "settling-place", "adherence" or, literally, "homes". As explained unambiguously in SN 22.79, when the Buddha recollected his "past abodes", he recollected when in the past his mind ignorantly clung to an aggregate as "self".

At Savatthi. “Bhikkhus, those ascetics and brahmins who recollect their manifold past abodes all recollect the five aggregates subject to clinging or a certain one among them. What five?

“When recollecting thus, bhikkhus: ‘I had such form in the past,’ it is just form that one recollects. When recollecting: ‘I had such a feeling in the past,’ it is just feeling that one recollects. When recollecting: ‘I had such a perception in the past,’ it is just perception that one recollects. When recollecting: ‘I had such volitional formations in the past,’ it is just volitional formations that one recollects. When recollecting: ‘I had such consciousness in the past,’ it is just consciousness that one recollects.

Therefore, bhikkhus, any kind of form whatsoever … Any kind of feeling whatsoever … Any kind of perception whatsoever … Any kind of volitional formations whatsoever … Any kind of consciousness whatsoever, whether past, future, or present, internal or external, gross or subtle, inferior or superior, far or near, all consciousness should be seen as it really is with correct wisdom thus: ‘This is not mine, this I am not, this is not my self.’

“This is called, bhikkhus, a noble disciple who dismantles and does not build up; who abandons and does not cling; who scatters and does not amass; who extinguishes and does not kindle.

“And what is it that he dismantles and does not build up? He dismantles form and does not build it up. He dismantles feeling … perception … volitional formations … consciousness and does not build it up.

SN 22.79

Ehipassiko, friends. Come & see, the real verifiable truth (of "re-birth") in the here-&-now.

You reconcile those two aspects of the dhamma by understanding that the dhamma is not about becoming a buddha, no matter what some intellectual puthujjanas claim, but about destroying dukkha, which turns out to have a condition for arising and a condition for cessation, so the goal is to trigger this condition for cessation.

When you are in the fourth jhana you can recollect your past lives and with the divine eye you can see devas and other realms. So it is not just blind faith. You can experience them here and now in this life. In DN 2, the Buddha explained the fruits of contemplative life.

"With his mind thus concentrated, purified, and bright, unblemished, free from defects, pliant, malleable, steady, and attained to imperturbability, he directs and inclines it to creating a mind-made body. From this body he creates another body, endowed with form, made of the mind, complete in all its parts, not inferior in its faculties. Just as if a man were to draw a reed from its sheath. The thought would occur to him: 'This is the sheath, this is the reed. The sheath is one thing, the reed another, but the reed has been drawn out from the sheath.' Or as if a man were to draw a sword from its scabbard. The thought would occur to him: 'This is the sword, this is the scabbard. The sword is one thing, the scabbard another, but the sword has been drawn out from the scabbard.' Or as if a man were to pull a snake out from its slough. The thought would occur to him: 'This is the snake, this is the slough. The snake is one thing, the slough another, but the snake has been pulled out from the slough.' In the same way — with his mind thus concentrated, purified, and bright, unblemished, free from defects, pliant, malleable, steady, and attained to imperturbability, the monk directs and inclines it to creating a mind-made body. From this body he creates another body, endowed with form, made of the mind, complete in all its parts, not inferior in its faculties.

"This, too, great king, is a fruit of the contemplative life, visible here and now, more excellent than the previous ones and more sublime. "With his mind thus concentrated, purified, and bright, unblemished, free from defects, pliant, malleable, steady, and attained to imperturbability, he directs and inclines it to the modes of supranormal powers. He wields manifold supranormal powers. Having been one he becomes many; having been many he becomes one. He appears. He vanishes. He goes unimpeded through walls, ramparts, and mountains as if through space. He dives in and out of the earth as if it were water. He walks on water without sinking as if it were dry land. Sitting cross-legged he flies through the air like a winged bird. With his hand he touches and strokes even the sun and moon, so mighty and powerful. He exercises influence with his body even as far as the Brahma worlds. Just as a skilled potter or his assistant could craft from well-prepared clay whatever kind of pottery vessel he likes, or as a skilled ivory-carver or his assistant could craft from well-prepared ivory any kind of ivory-work he likes, or as a skilled goldsmith or his assistant could craft from well-prepared gold any kind of gold article he likes; in the same way — with his mind thus concentrated, purified, and bright, unblemished, free from defects, pliant, malleable, steady, and attained to imperturbability — the monk directs and inclines it to the modes of supranormal powers... He exercises influence with his body even as far as the Brahma worlds.

"This, too, great king, is a fruit of the contemplative life, visible here and now, more excellent than the previous ones and more sublime. "With his mind thus concentrated, purified, and bright, unblemished, free from defects, pliant, malleable, steady, and attained to imperturbability, he directs and inclines it to knowledge of the recollection of past lives (lit: previous homes). He recollects his manifold past lives, i.e., one birth, two births, three births, four, five, ten, twenty, thirty, forty, fifty, one hundred, one thousand, one hundred thousand, many aeons of cosmic contraction, many aeons of cosmic expansion, many aeons of cosmic contraction and expansion, [recollecting], 'There I had such a name, belonged to such a clan, had such an appearance. Such was my food, such my experience of pleasure and pain, such the end of my life. Passing away from that state, I re-arose there. There too I had such a name, belonged to such a clan, had such an appearance. Such was my food, such my experience of pleasure and pain, such the end of my life. Passing away from that state, I re-arose here.' Thus he recollects his manifold past lives in their modes and details. Just as if a man were to go from his home village to another village, and then from that village to yet another village, and then from that village back to his home village. The thought would occur to him, 'I went from my home village to that village over there. There I stood in such a way, sat in such a way, talked in such a way, and remained silent in such a way. From that village I went to that village over there, and there I stood in such a way, sat in such a way, talked in such a way, and remained silent in such a way. From that village I came back home.' In the same way — with his mind thus concentrated, purified, and bright, unblemished, free from defects, pliant, malleable, steady, and attained to imperturbability — the monk directs and inclines it to knowledge of the recollection of past lives. He recollects his manifold past lives... in their modes and details.

"This, too, great king, is a fruit of the contemplative life, visible here and now, more excellent than the previous ones and more sublime. "With his mind thus concentrated, purified, and bright, unblemished, free from defects, pliant, malleable, steady, and attained to imperturbability, he directs and inclines it to knowledge of the passing away and re-appearance of beings. He sees — by means of the divine eye, purified and surpassing the human — beings passing away and re-appearing, and he discerns how they are inferior and superior, beautiful and ugly, fortunate and unfortunate in accordance with their kamma: 'These beings — who were endowed with bad conduct of body, speech, and mind, who reviled the noble ones, held wrong views and undertook actions under the influence of wrong views — with the break-up of the body, after death, have re-appeared in the plane of deprivation, the bad destination, the lower realms, in hell. But these beings — who were endowed with good conduct of body, speech, and mind, who did not revile the noble ones, who held right views and undertook actions under the influence of right views — with the break-up of the body, after death, have re-appeared in the good destinations, in the heavenly world.' Thus — by means of the divine eye, purified and surpassing the human — he sees beings passing away and re-appearing, and he discerns how they are inferior and superior, beautiful and ugly, fortunate and unfortunate in accordance with their kamma. Just as if there were a tall building in the central square [of a town], and a man with good eyesight standing on top of it were to see people entering a house, leaving it, walking along the street, and sitting in the central square. The thought would occur to him, 'These people are entering a house, leaving it, walking along the streets, and sitting in the central square.' In the same way — with his mind thus concentrated, purified, and bright, unblemished, free from defects, pliant, malleable, steady, and attained to imperturbability — the monk directs and inclines it to knowledge of the passing away and re-appearance of beings. He sees — by means of the divine eye, purified and surpassing the human — beings passing away and re-appearing, and he discerns how they are inferior and superior, beautiful and ugly, fortunate and unfortunate in accordance with their kamma...

"This, too, great king, is a fruit of the contemplative life, visible here and now, more excellent than the previous ones and more sublime.

The last one is about karma so it’s possible to understand karma. It is one of the fruits of contemplative life. If you don’t believe in these things then meditate and master the fourth jhana.

In this sutta (https://www.accesstoinsight.org/tipitaka/an/an04/an04.077.than.html), it is explained that the power of Gotama Buddha as a sammasambuddha cannot or should not be conjecture about; the underlying mechanisms of kamma are not available to be investigated either. However, also in the suttas it is emphazised that the teachings can be tested by ourselves through practice and investigation, being that the 'ehipassiko' ("come and see") aspect of the Dhamma.

I don't see any contradiction in the suttas. Sorta like a college math professor telling 5th graders not to conjecture about the working of calculus, differential equations, etc. But once the students have made it thru high school and into college, taking more advanced math and they'll be able to "come and see" and find out for themselves. Similarly, there're many things in the Dhamma that can be verified, some can be verified in the here and now, some would require thorough training with much dedication and effort down the line.