Ron - if my friend's ancestor had been an officer (they mostly belonged to the landed gentry), he could have sent his son to university by his own means.
My friend had explicitely stated that his ancestor was a peasant. Don't forget that the Hessian soldiers got double pay, and over the seven years of the war they sent back the money they didn't need in the colonies, because they were accustomed to a thrifty life. The several hundred thousands of Thalers (americanized to dollars) were a big kick to the economy of Hessen-Kassel and the forthcoming of many a family.
I'm from a peasant's family too, but my ancestor had a big inn besides at the great road from Hamburg to Basel, and the eldest son inherited the farm; the younger ones had to go to university. So since the beginning of the 18th century my ancestors were mostly ministers. The entrance into academic life of peasants' or craftsmen's sons was always the theological faculty, and the studies of qualified theologicians were often supported by The Fund (an endowment of the late Landgrave Philipp). You had to get only a small capital to get to a start.

The State of Hessen-Kassel had a lot of treaties for mutual military support with several other states, e.g. Sweden since the 30 years war. The treaty which paid best was the treaty with the British Crown, often renewed. The Crown paid most of the expenses of the Hessian army in peacetime, and when needed the army marched to support the British army. Sometimes it was the other way round. So the Hessian soldiers were not REPEAT NOT mercenaries, but members of a regular army bound by treaty to support a friendly army (like NATO today - any soldier of the NATO would be highly insulted if you called him mercenary when fighting side by side with his allies).
In your post I find a lot of the usual anti-Hessian propaganda; about 1866 some of it was repeated by the Prussians who finally annected this state because of its riches which stemmed from the American war (the robbed treasure was kept by the Prussians to the beginnings of the 1920s when it dwindled away during the inflation).

Your remarks about the parallel to the war in VN I found very interesting. The experiences Hessian and other officers had made with a people's liberation war were not without fruit. The uprisings against French rule in 1809 were incited mostly by veterans of the American war. Unfortunately the time wasn't ripe, but in 1813 they succeeded.