Sure. Just pop that puppy out and see what happens. I was just talking from a perspective of every little thing being a possible culprit, but it sounds like you've got it more narrowed down already.
You can even pull the rear shaft and run it in 4-wheel high for a bit to see what happens. Good to experiment.
And yes, the Dana 20 is an excellent case for a Bronco. The best? Probably not. But the best bang-for-the-buck? Probably.
Good and strong gear drive. Reliable to a fault, except when you start going radical with tire size and engine torque and vehicle weight. Or when it runs out of oil!!! Hah! I think we've got your demon right there. Could have been low for a long time for all you know. Or leaked out before, then run for a long time, then re-filled by the PO just before you bought it. No way to tell.
The big "weak link" if you can call it that, is the rear output section breaking on a lot of the guys here. Then again, it's usually those that do heavy wheeling with larger tires and more torque or heavier rigs. Not always, but certainly a trend.
Most of us, on the other hand, are doing just fine with ours.
A more modern unit, like an NV231 or 241 would be quieter, have more aftermarket support, have slightly lower gearing, and can be bought with lower gears still.
But nothing wrong with working with the one you have. At least far enough to find out if the case or gears are shot beyond repair.
Good luck in that department.
Paul