#1 Well, um, that button wouldn't be very useful. But you could set it to sysex, but I don't think that's what you want.
#2 Yeah, just reverse the MIDI OFF and ON of the momentary and then make it send on only
#3 However, I think your earlier comment does give us some hope. Since a Button Group super can force the button group to be send-on only, you might be in luck. Well... actually I don't know, there's a lot to experiment with.
At the risk of stating the obvious in a clearly advanced conversation: save your real layout and mess around in a sandbox where you can test your concepts very easily, with a tiny set of throwaway controls. The LOG will help you know what's going out when. Much easier than working on your actual rig, IMHO.