I think someone here (Oscar?) posted that the Happ Supers (and all the other IL joysticks) have 10mm shafts whereas the old Wico leafs and the Perfect 360s have 9.5mm shafts.
It might not sound much of a difference but it is enough apparently for the Super handles not to fit the Perfect 360 and Wico bases.
You could however fit Wico ball top (and presumably also Wico bat top) handles to a Perfect 360 base if you don't like the shape of the standard handle.