OK, I bought the StM32F7...Discovery board and, sure enough, ADAcore GNAT has support for it. I'm just starting to look at the package but from what I can see, "Hello World" even when linked with the "small footprint" library is ginormous, on the order of 140k, if I am looking at the correct output file.
Anyway, the board will be here in a few days. Now what?