You do not have to remove the springs to take the rear bumper off.
You also don't really have to take the bumper off of its brackets.
You can remove the bumper complete with its brackets, if you can get a wrench in there. It's a nuisance, but can be done, especially if you have access to a 3/8 inch drive pneumatic ratchet. Unless someone has messed things up, those nuts are captive, and you do not need access to them. Take your time, get lots of penetrant, wiggle back and forth if necessary, to avoid snapping the captive nuts free or shearing off the bolts, and you should be all right. I've taken bumpers off some very rusty Jeeps without disaster.
Once the bumper is off, you slide the nut strips right in from the end.
If you're willing to saw a hole in the bumper, why not grind, saw or flame cut the offending bolt heads off instead? After the bumper is off you can remove the remains of the bolts and the broken spring nuts.
It is, without doubt, an annoying design - the spring nuts are unreliable, and the lack of even rudimentary stock tow points is hard to understand, but once you have a hitch, you'll be set.