Tanha vs "Right Aspiration" & Anatta vs nihilism: how does one resolve contradictions in BUddhism?

Annata and enlightenment

The Aggi-Vacchagotta Sutta gives an answer of sorts as to what happens to the Buddha after he dies. A summary of the sutta might be that any view about what happens after the death of an enlightened being is wrong-view because that being didn't ultimately exist before death (you should read the sutta yourself to get a more full understanding).

The only option for a mind made illusion is to simply cease to exist

I don't think that this is a problematic position on the issue. There's a distinction made between a self which didn't inherently exist before or after enlightenment, and the illusion of self which existed before enlightenment but not after. Annata is about the self whereas enlightenment is about the illusion.

You object to the idea of the illusion being enlightened or saved but this is really just a problem with semantics, you think that the word "saved" has to refer to something real which is saved but when we use this term in Buddhism we used a more flexible definition and it's only the illusion of self which was suffering that is now saved.

Craving and right-aspiration

Clearly Buddha did not condemn "desire" if you define it as wanting something you don't have. So what distinguishes between the two?

There are two Pali words tanha and chanda. Chanda is a sense of wanting which arises in the mind before the defilements turn it into tanha which is the craving that leads to dukkha. When chanda arises we can use wisdom to decide whether to follow a want or not, if we have no wisdom then when chanda arises we immediately attach to it and think that our wants have to be met and so we suffer. If chanda arises and the wanting is right-aspiration then we choose to follow that thought, however, we don't attach to it so that when our efforts don't get us what we wanted we don't suffer.

This is a difficult distinction to see, an example of how we can treat chanda with wisdom might help.

Imagine that you see a starving man and there is a wanting (chanda) to give him food. You know that you don't have control over the world and limited control over your body so you can only attempt to give him food. You pick up some rice and walk towards him but your hip dislocates and you can't walk to the man so he starves.

In this example from the moment the chanda arose you knew that you could only attempt to feed the man so there was no attachment to the result of your actions. This line of thinking didn't lead to a craving for the man to be fed and so there was no dukkha as a result.

So what distinguishes between the two?

Maybe one thing that distinguishes it is whether it is "Right".

Right Aspirations follows from Right View, whereas presumably Tanha does not follow from right view.

It's easy to find explanations, e.g. here's the first thing I found via a Google for "right aspiration":

It is important to see that aspiration is not desire. The Pali word ‘tanha’ means desire that comes out of ignorance, whereas ‘sankappa’ means aspiration not coming from ignorance. Aspiration might seem like a kind of desire to us because in English we use the word ‘desire’ for everything of that nature - either aspiring or wanting. You might think that aspiration is a kind of tanha, wanting to become enlightened (bhava tanha) - but samma sankappa comes from Right Understanding, seeing clearly. It is not wanting to become anything; it is not the desire to become an enlightened person. With Right Understanding, that whole illusion and way of thinking no longer makes sense.

There's also a sutta whose topic is the question you asked: Brahmana Sutta (SN 51.15)

Anatta doctrine held by some Buddhist

I think it's held by all Buddhists.

It's listed in this answer to 'What teachings do all schools of Buddhism share?':

7. We understand, according to the teaching of the Buddha, that all conditioned things (samkhara) are impermanent (anicca) and imperfect and unsatisfactory (dukkha), and all conditioned and unconditioned things (dhamma) are without self (anatta)

nothing really "exists"

That might be a mis-statement of the doctrine. See for example this Zen story: Nothing Exists

is basically nihilist

I think that what Buddhism describes as "nihilism" is the belief that actions have no consequence; or a "nihilist" might be used to describe someone with no doctrine at all.

you are doomed to the grave

That's implying there's a "you"; or that the body which is destined for the grave is you.

I think that Buddhism teaches that views-of-self (ego-centrism, identity-view) lead to suffering, and that it's therefore better not to hold to such views.

The only option for a mind made illusion is to simply cease

Maybe. Apparently sometimes the "ego" struggles against "ego death"? Those are words that I read sometimes, see e.g. Ego death - Buddhism.

I suppose it's obvious that illusions do come and go; no big deal.

Or maybe illusion doesn't cease.

How do you resolve this seeming contradiction?

Apart from the Anatta-lakkhana Sutta, I also recommend paragraph 23 of the The Discourse on the Snake Simile (MN 22):

23. "You may well accept, monks, the assumption of a self-theory from the acceptance of which there would not arise sorrow and lamentation, pain, grief, and despair. (But) do you see, monks, any such assumption of a self-theory?" — "No, Lord." — "Well, monks, I, too, do not see any such assumption of a self-theory from the acceptance of which there would not arise sorrow and lamentation, pain, grief and despair."

Anatta doctrine held by some Buddhist, that there ultimately is no-soul or self

Correct.

and nothing really "exists"

Incorrect. Mind & body exist. Five aggregates exist. Nibbana exists.

but is empty of inherent existence

Empty of 'self' existence. Empty of permanent existence. But exist temporarily.

and therefore insubstantial

The five aggregates are 'insubstantial' due to their impermanence. But not Nibbana.

and suffering

This is a mistranslation. In respect to the five aggregates, the translation is 'unsatisfactory' because impermanent things cannot bring lasting happiness.

is basically nihilist.

In Buddhism, 'nihilism' refers to the (wrong non-Buddhist) view that there is a 'self' that ends at death. Since Buddhism explains there is no self to die, it is not nihilist.

This contradicts Buddha's teaching on rebirth

'Rebirth' refers to the re-arising of 'self-view' due to ignorance. There is no contradiction.

and Nirvana (the unborn, unmade, unconditioned etc. makes liberation from the born, made, conditioned possible).

Nirvana is the peace that is known by the mind when 'self-view' & craving end. There is no contradiction.

No matter how you want to spin it, if your position is that the soul does not exists and there is no self outside of conditioned existence, then you are doomed to the grave and there is zero possibility for enlightenment or liberation from Samsara

'Samsara' simply refers to the mind spinning around in 'self-views' due to craving & ignorance.

because how can an "illusion" that doesn't exists be "enlightened" or "saved"?

What is saved is the 'mind'. In Buddhism, it is called 'ceto-vimutti', which means 'mind-liberation'. When the mind is cleansed of greed, hatred & delusion, it is 'saved'. That the mind has a illusory quality is irrelevant to this salvation.

The only option for a mind made illusion is to simply cease to exist once the causes that create the illusion (the body 5 kandas etc.) dies.

The mind is an illusion rather than life. For example, the planet earth is not really an illusion. It is only the mental perceptions (of earth) that are 'illusory'. The earth is very solid and has existed for billions of years. But the mind exists for moment, ceases & then arises for another illusory impermanent fleeting moment.

You just fade to black, no karma, no rebirth, no Nirvana, no enlightenment no nothing. How do you resolve this seeming contradiction?

Yes. It can seem to be like a 'contradiction'. But when the mind is free from greed, hatred & delusion, what seems to be 'contradictory' to an ignorant unenlightened mind will vanish.

The Buddha was never under the illusion that all individuals could comprehend his Dhamma.