I am NOT an expert on this, but one thing I noticed I'm not certain is correct is using the "lifted" version of the JBA upper arms with the OME lift.
I believe the shortness of the left side CRD axle limits lifts to the point that the "lifted" versions are not necessary.
I am sure tommudd will correct this if it's wrong, but it might be something to examine.

I'd be interested to hear what he has to say - JBA is selling the OME lifts as a package with the upper arms, and I specifically bought that package with an eye towards possibly adding another inch or so onto it in the future.

My guess is that caster would be the issue in this case (particularly with the relatively small lift), but that should probably be able to be corrected with shimming at the upper ball joints.

JBA offers 2 sets of upper arms.

Stock to less than 4" lift.
4"+ lift

I've always gotten the gist that 4" with a CRD would cause problems with the CVs on the left side, due to the shortness of the axle.

Which rims you are using? Front wheels with less offset cause car to "search" in uneven surface more than stock ones. I personally have rims with 18mm less offset than originals and it is bit more sensitive but not disturbingly lot. I have 1.5" H&R springs with original upper arms and after alignment it is even more stable on road than before the lift.

Have you tried if it's the same with four wheel drive? If connecting 4x4 calms it, there's most probably too much negative toe-in.

I'm guessing they are not the ones recommended for an OME lift.

Whether or not they would cause any issues, would take someone far more knowledgeable than I to answer. You could try calling JBA, or wait for Mr Mudd.

Someone once posted the alignment specs for a lifted liberty. I cant remember exactly what they are. But basically, caster doesn't get adjusted. The lift will cause caster to be a bit out of spec. It just is what it is.
Camber and toe is only what gets adjusted.
All adjustments are done at the lower control arm and tie rod ends. Nothing to adjust with the upper arms.

When I did my lift, I marked the lower cam bolts, then loosened them.
When I had it all back together, I set the cam bolts back to their marked location and tightened them up with the full weight of the jeep on the ground.
All the alignment shop had to do was set the toe.
It pulls a bit to the right but other than that it steers pretty good. Steering is a bit more sensitive because of the increased angle of the tie rods between the rack and steering knuckle.

I will say that the JBA upper arms are necessary for doing the lift.
I thought my lift wouldn't be too much for stock arms, but 8 months later my upper ball joints are showing wear and need replacement.

BTW, if steering still seems too sensitive for you, bigger wider tires will help dampen that feeling

Interesting. OK, that pretty much eliminates caster as a possibility.

Caster is a major possibility.

For the IFS KJ when doing a alignment after a lift you want the camber to be set in spec(with no more than 0.5 degree cross camber),toe is set to spec,and caster is the compromise but needs to be at least 2.5 degrees and no more then 0.5 degree cross caster.Caster and camber are both adjusted via the LCA cam bolts and moving 1 bolt effects both measurements but the front effect camber more while the rear effects caster more.

Less caster = easier slow speed turning,twitchy high speed steering(sensitive at higher speed)

More caster = harder slow speed turning but much better control and less sensitive at higher speeds.

Your typical Jeep and or pickups have between 2.5-5 degrees of caster,your typical passenger car has 3-6 degrees of caster,and your higher end "touring" cars will have 6-10 degrees of caster.

Have you tried rotating the tires? possible you are fighting a 'wear pattern' from previous set up.. These are the tires from pre lift days?
I'd let it settle-in for a couple thousand miles, and return for another alignment.

I may end up farming this part of it out. I'm not sure that I can get it sufficiently in range with what I have to work with in the driveway.

It's impossible to set camber/caster in your driveway without a alignment rack.