Ok, I see what you're saying now.
PRP26A will fit in there, but its an expensive solution for one rivet. If you were in DFW I'd loan you mine.
Silly question, but have you tried putting the rivet in the puller first, opened the puller all the way, give a gentle squeeze but stopping just before the rivet starts to distort, and then put the rivet in the hole? You may need to gently flex the bulkhead on the other side out of the way some.
EAA chapter near by? If you could borrow a rivet gun and bucking bar, that might work. You'd have to back rivet it and the F12107B might be in the way.