I was reluctant to use Catweasel because you can't boot real Amiga games on the PC but didn't know it had Keyrah style built in joysticks.
True, you can't boot real Amiga games.
But you
can WHDload install them from the floppies. You just need a bit of software imagination and gratuitous use of NSDPatch.
If you can get a Catweasel in there, you can install your Amiga floppy originals and play them with real Amiga joysticks (and mice). You'll need a PCI slot though, that's going to be the problem.... but it wouldn't need to be externally accessible. You could just run a lead from the internal joystick ports to 9-pin ports mounted in the case, just like in the real Amigas.