That doesn't give trigger or thumb buttons, though, so going that way puts it 6 or 7 buttons, not 4. The trigger joystick is the best way I have come up with so far to have that many distinct controls in one spot.
What I may have to compromise here, though, is finding a smaller trigger joystick. Since this isn't a commercial cab, if the Happ stick turns out to be too big, I can find a decent 8 way PC trigger joystick to use. That would actually be easier to interface, too.