I know that your past this part but sometimes instead of using a pic to turn the broke off bolt, the other half of the bolt might snag on the part still in differential. I would think that using heat on the carrier where the broke off bolt is still in the carrier would help release the lock-tight glue.
A press or air chisel might could be used to shear the bolt where it goes through the big pin. That's a hopeful thought if the bolt broke so easy in the first place. At some point the carrier will get damaged. At that point it can get really ugly trying to save the good housing and axles.
I had a 1992 7.5 Mustang pin that would not come out. I ended up swapping in a whole different differential assembly.
I hope your diffy is up on a work bench to deal with it.