Why are some school systems from September–July versus others that go April–March?

That seems pretty much like asking why most countries force their people to drive on the right side of the road, when left driving is clearly superior. Or vice versa.

It's pure historical contingency, then path dependency mixed with convention and afterthought rationalisation (like here). It could have been switched at any time to an arbitrary date. Just like the real calendar. Since when is January 1st 'the start of the year'?

As already noted, in Germany it was not always in autumn – but in contrast to the proposed reasoning of "late founding/labour regulations" – the dates remained pretty chaotic, varying between states, until very recently. That should read: it is now standardised to 'all begin in late summer/fall none in spring'. The exact starting dates vary still from state to state and from year to year!

Previously, school years started in spring around Easter, or in September, and starting dates even switched around from time to time.

'Harvest' cannot have played a decisive role there and then, as should be obvious from the switching and the stretched out times to cut summer corn or winter corn, vegetables or potatoes etc.

If 'harvest' was important, that was sometimes synchronised with holidays, or simply afforded for those still in need of it as 'days off on the fields', beet holidays, potato holidays etc) but it did not play a role for the administrative divisions or alignments.

Compare "Senioren erinnern sich an ihre Kartoffelferien Für jeden Korb gab‘s Kirmesgeld" (Senior citizens remember their potato holidays. For every basket there was fair money):

Autumn time is harvest time, but also time for holidays. While today's students enjoy 14 days off, things were quite different in the war and post-war years. Because the autumn holidays used to be called "potato holidays", and there was a reason for that. "We went out into the fields… We searched with our hands and dug up potatoes," Maria Vormann remembers.

Note that whether Easter/Spring/April start or Autumn/September start, this harvest would always fall afoul of any such date. Consequently, the official harvest festival is dated to first Sunday of October (with a historical range of setting the date anything between August 24, Bartholomew Day, and November 11, Martini).

A summary of the state of affairs in Germany is provided on WP:

In the Empire and the Weimar Republic, the beginning and end of the school year were not uniformly regulated. The school year began partly after the summer holidays, as in many other European countries, but partly also in spring (Easter). In 1920 the start of the school year in Bavaria was changed from summer to Easter.

In 1941, the start of the school year was set at September throughout the German Reich. This was reversed after the Second World War by the occupying power in the British zone and, except in Bavaria (American occupation zone), also in all other countries in the western occupation zones, as their ministers of education decided almost unanimously in August 1948. In Hesse, for example, the school year 1947/1948 was extended by one half-year, so that it ended at Easter 1949. In Saarland, too, the start of school was moved from autumn to spring after the integration into the Federal Republic (January 1, 1957). The Düsseldorf Agreement (1955) of the Conference of Ministers of Education and Cultural Affairs had recommended this without success, even to Bavaria.

And when the school year starting dates were about to be harmonised, within Germany – and – within Europe (EEC etc) we see this:

The experts agreed that the best time for school children to work is between September and December. "The annual curve of adolescent performance," as psychology professor Willy Hellpach had already noted in 1939,

"reveals to us... a physical and mental low in midsummer, a physical and mental high in early winter, a physical high with a mental low throughout the spring, already beginning in late winter and leading into the midsummer double low.

However, different conclusions were drawn from the results of the high and low research. As the Standing Conference of the Ministers of Culture noted, "basically two different pedagogical views and teaching methods" clashed on each other:

• The Easter Party wants to place the high between September and Christmas in the second half of the school year so that the children can concentrate on the exams.

• The Autumn Party, on the other hand, wants to use the students' autumnal energy to teach them the main part of the material in the first part of the school year.

According to an enraged autumn advocate named Grimm, headmaster in Tutzing, it is important that "the teacher reaches his judgement through constant work with the pupils". The "predominance of written works" must be broken, he said, because they are "a terrible and mind-boggling, time-consuming burden for the teachers and an unheard-of nervous strain for the students."

Relief was promised by a reformer by the name of Schuh, headmaster in Munich, also in another respect: "The summer holidays would become the natural boundary between two school years", and if "the pupil had failed, the uncertainty need not be dragged through the whole summer time; if he had passed, his satisfaction was all the more justified. In any case, a psychological pressure has disappeared".

In 1962, when the CDU factions of all the state parliaments pleaded for a change in the school seasons, hopes for the autumn spread more and more. The teachers' union, the philologists' association, and several ministers of education, including the SPD-Voigt of Lower Saxony, who was in office at the time, and his Hessian party friend Schütte, immediately agreed.

And Bremen's SPD Senator for Education, Dehnkamp, no longer considered it appropriate to enrol young Germans on the same date as Panamanians, Thais and Peruvians instead of at the same time as almost all children between the Bay of Biscay and the Urals. Dehnkamp: "If you want Europe, you must also agree to start school together in autumn."

In Hamburg, which is otherwise cosmopolitan, people had a different opinion. Main argument: the change of the dates would mean the end of the so-called open-air education. Hamburg's pupils are accustomed to taking a one- or two-week class trip every two years, especially in the seasons that are to be burdened with the first weeks of school (in August/September) or with examinations (in May/June).

Only "for the sake of the uniformity of the German school system" Hamburg's Senator for Education Drexelius agreed to the new regulation last week. Leap years for the changeover: 1966 and 1967.

Even then, however, the country will still not be connected to Europe. In almost all countries on the continent, the summer holidays are considerably longer than in the Federal Republic.
_{— "Tüten im August", Der Spiegel, 04.11.1964.}

As noted, the above article is from 1964 and couldn't imagine that in West-Berlin the Easter start date remained guaranteed for all those that had started school on Easter dating until 1976, in parallel to those elementary pupils starting their school year in September since 1966.

Now that the harvest myth should be destroyed, we might look at a deeper aspect of analysis, albeit of much the same quality as before:

Some calendars used the moon’s phases as their unwritten pages, often basing the names of the full moons on the natural phenomena and accompanying human activities that occurred about them; so we could say their years had twelve or even thirteen seasons. Contrast this with the seasons we live by today, which begin on Labor Day (the start of the work/school cycle), July or June 1 (the start of the fiscal year), or the many “openers” in the seasonal sport cycle. […]

America’s summer ends on Labor Day, three weeks before the au- tumn equinox, just as it begins on Memorial Day three weeks before the June solstice (or May Day in most of the rest of the Western world). Leisure done with as August draws to a close, we all look forward (usu- ally with dread if we’re schoolkids) to the week that follows—a time band headed by a day that has come to symbolize putting away our play- things and getting back to work. As a kid I remember asking myself: if fall doesn’t begin until September 23, then what am I doing back in school when I should still be on summer vacation?

If Independence Day masquerades as our summer solstice, then Labor Day surely is our equinoctial “New Year.” It signals the start of an anxious season, a short in-between time that is neither summer nor fall, but shares aspects of each. Labor Day is a conflict of interests.
_{— Anthony F. Aveni: "The Book of the Year: A Brief History of Our Seasonal Holidays", Oxford University Press: Oxford, New York, 2003.}