Had any tire work done lately?
Reason I ask is that a difference in tire size (even same size tires but different brands) can cause what you are experiencing. If you have 2 tires that are worn and 2 that are new, replacing the 2 older tires with the same ones as the new ones would be my call.
If all your tires are the same, check the inflation levels.
As far as the vehicle fighting itself in 4wd on pavement, well, yes. It's a part time system and the front and rear driveshafts are turning at the same rate. When you turn, the outside front tire moves quite a bit further than the inside rear tire, resulting in the driveline binding up. Damage can occur, so turning on a non-slippery surface is not recommended (owner's manual has details on this).
So...check tire pressure, tire manufacturer and wear of all tires. You might get away with a tire rotation only, but can't know the answer to that until you have looked at them. Post back with the results and we'll try to help some more.
edit: another thought. At 127k, if you've never changed the transfer case fluid, that could contribute to it sticking in 4wd. Pretty easy job, just need some lube, something to pump it with, and the right tools to open up the plugs.