Most garages have an induction heat tool which makes light work of seized nuts/bolts.
I use mine on a regular basis but I still sometimes revert to the old tried and trusted oxy/acc method, however with the confined space of the diff nut the induction method works great.
Removing the bushing can be a messy job as you know, but once you put a cut in the outer shell it will just fall out.
Remember and stick your new solid bush in the fridge/freezer overnight