My iCade worked just fine with the two MAME apps I got from the App Store (iMAME and Gridlee), but it didn't work with the MAME apps on Cydia!
However, iMAME4all now has this in the description:
"Added iOS 6.x compatibility (fix iCade)"
I'm loading this up to try again:
iMAME4all
MAME4iOS Reloaded
mame4iphone
Edit: looks like iMAME4all and MAME4iOS Reloaded work with my iCade.
At least, they see button pushes now.