Ok, so if a stiffer rear sway bar increases oversteer, then I may need to experiment with disconnecting the rear sway bar, which should decrease oversteer. If it improves the oversteer, but induces understeer, I may need a rear sway bar that is less stiff than stock. A rear Anti-rock to match the front Anti-rock might be what I need. That seems counter intuitive though, because it feels like the rear end is leaning too much in turns. Maybe I'm misinterpreting what I feel as oversteer, when it isn't. When you enter a turn, and the rear of the Jeep starts to lean, you have to turn the steering wheel back toward center somewhat, to decrease the steering input, or you will tend to turn too much. That sounds like oversteer to me.
My last lifted Jeep had an AEV lift on it, but it was a four door JK, and not a two door, so maybe not quite comparable with handling. The rear of that Jeep cornered flatter, but the front leaned more than my current Jeep. Overall I would say they were about even in handling, with the edge going to the four door, probably just because it was a four door.
Yes, we are talking about a Jeep. I don't expect great handling, but if I could get better handling with a little tweaking here and there it would be worth trying.