As far as I know, superdeterminism in quantum mechanics is only considered as a theoretical possibility. Are there any fleshed out superdeterministic toy models so far which isn't nonlocal?
Yes. Bohmian mechanics is superdeterministic. You see, the pilot wave and the "particle" covers everything in the universe, including the experimentalist and the measuring apparatus. The location of the "particle" fixes the experimentalist's will and the detector settings superdeterministically. Neither the experimentalist nor the detector has any free will in bohmian mechanics.
Superdeterminism is really more conceptual than something you can flesh out. The Wikipedia article you link has a good quote in this regard:
[W]e always implicitly assume the freedom of the experimentalist... This fundamental assumption is essential to doing science. If this were not true, then, I suggest, it would make no sense at all to ask nature questions in an experiment, since then nature could determine what our questions are, and that could guide our questions such that we arrive at a false picture of nature.
Similar possibilities that are a bit more interesting however are so-called supercorrelating interpretations, which Louis Vervoort gives an explanation of here (as well as a longer explanation of superdeterminism you might find interesting); DOI: 10.1007/s10701-013-9715-7.