Like said, it can still be the locker unfortunately. At the very least, it's acting to exaggerate another issue, but it's likely to be at least part of the trouble. No matter what, you should optimize everything else to be sure.
I've driven plenty of trucks and Broncos with Detroits before, with very minimal or at least the expected issues. Usually no problem, as the other users are saying.
A friend had a '75 with Goodyear MT's and it was literally un-drivable. Each time you would let off the gas and push in the clutch to shift gears, it would literally try to swap lanes on you. He actually drove it to my house so I could test drive it to help diagnose the issue we had been discussing over the phone, and I only got out of the driveway and a few yards down the street before I decided that we were only going around the short block!
Brought it right back and a misbehaving locker was the only thing I could think of that would make a Bronco feel and act like that. Without changing anything else, he swapped it out for a Truetrack and any issues were immediately gone. To the tune of about 95%.
His truck was still a little loosy goosy with all that lift and such, but it no longer tried to kill him when driving.
Funny about the same tire in these two cases. Did you also buy one of those less expensive eBay Detroits that are supposedly Nascar units?
Paul