Holy cow! No kidding, a hidden help menu! And you the man @CalS, that did it! I disabled the HTTP Request Batching, closed Evernote (it ran a sync that didn't fail), reopened, re-enabled HTTP Request Batching and finally attempted a re-sync. And it worked! I guess the "Excessive batch response size" error might have been a clue, though I never would have guessed there was a hidden help menu.
Many thanks!