Tried the AGA core and kickstart 3.1 again. Managed to get into the minimig menu and changed the CPU to 020 Alpha. And now that setup works
Glad to hear it's working. The "perfect" ROM for Minimig is actually the 3.1 A600 ROM because it works with all CPU settings, but still supports hard drive and AGA graphics!
I shall have a look at defaults in future - you're right, 68000 / ECS is probably not the best default setting, even though the core's intended to be ECS and AGA, not AGA only.
Real A500 keyboards aren't yet supported, but are on the "To Do" list.
Thanks for the reports of non-working games - there are a couple of other compatibility issues that I'm aware of - but please let me know if you find any more.