I've tested in a IIgs at 2.8 MHz. Maybe that isn't fast enough to show the problem, or maybe the issue is unrelated to speed. When AmpArcade crashes, what happens? Does it break to the monitor? If so, what's the program counter, and what data is at that address?
AmpArcade tends to crash if it's unable to detect the card. Maybe there's a bug in the detection logic. Also, AmpArcade scans slots to find the card, and the scan process involves writing to whatever cards are in your slots. That could "mess up" other cards. What happens if you move the AppleTi to slot 7 (the first slot in the scan sequence)?
Many of the AmpArcade and SuperSprite demos do not work with the AppleTi. Those vintage cards include sound and video mixing hardware. When the software attempts to write to that non-existent hardware, you end up with random writes to the F18A registers. That has various odd effects. You might be seeing these effects -- you'd have to remove sound and video mixing hardware accesses from the demo to confirm this theory. Or, if the demos use AmpArcade rather than direct POKEs, we could disable the unsupported commands in AmpArcade.
I'll investigate the software side. I do plan to extend AmpArcade with F18A-specific features, but, like all hobby projects, that might take awhile.