Massive caster variance Side to side

I won't pretend to know your problem(s), but like Rusty, I spent many years doing alignments in a tireshop. So I can tell you how to figure it out, hopefully in the least frustrating way. Here goes.
I always check the CASTER first at Zero-CAMBER.
Caster you know, so lets look at camber.

In order to check the camber;
> both lower BJs need to be on the same imaginary transverse line that runs from one side of the car, thru the centers of both inner pivots, to the other side, at 90* to the centerline of the car, and
> the center of each LBJ needs to be equidistant from the centerline of the car,
> and the center of both lower BJs need to be at the same distance from the ground, and
> both spindles need to be pointing away from the centerline of the car, at 90*

Thus, the engine-cradle/K-member, which carries the Control arms, in which the LBJs are mounted, has to be square and centered between the frame rails, assuming the rails are in the correct spots.
If the car has had it's frame tweaked, good luck with that. Now you have to "string" the car on a dead flat groundplain.
Next, the K has to be leveled in front view, where they are screwed to the framestubs.
Then the LBJs have to be adjusted to be in the right place, using the Strutrods, and set to the same vertical height from the ground plain.
This now is your reference. From here, the UCA is manipulated, to make the other angles accurate.

I always start with finding the maximum caster at exactly zero camber;
If the two sides are more than one-half a degree different, I go hunting for why.
If I can't get zero camber, I go looking for why.
If I can't get positive caster, I want to know why.
>Only after the caster has been bugged out, do I adjust the camber. Now, as to setting the camber, you have to set the ride height first, to near the factory specified height, in order to minimize camber changes when the suspension changes, while driving in the straight ahead direction; which camber change causes a toe-change, which is witnessed as wandering, or even a pull.
Failure to set the ride height correctly, is a sure way to waste your time messing with your alignment. If you need your ride height to be other than factory, you use tire size or rear spring arch, NOT the T-bar adjusters. Well, you can if you are in or near, the center of the camber-change/bump-steer, window)
If you have one weak spring on the back; then, to level the car in side to side, you will have to crank the T-bars differently, which will raise/lower the inboard reference of each LCA, putting the LCAs in different parts of the camber-gain window. Don't do that, get new springs first, then do the alignment. Or, in a pinch, jack up the rear end on a pivot pin in the center of the banjo, until the rear frames are equidistant from the ground plain; then adjust the T-bar preload, then go back and recheck the rear frame height, as many times as necessary to get it right. Once both ends are leveled, in side-to-side, then you can begin, from the beginning. Honestly, as soon as you put the rear of the car back on the ground, your alignment will take a sheite, so just get new springs, or fix the old ones..
In order to get more caster, for whatever reason, you can use the Moog Bushings. But if you have camber problems before the install, you will only have the same problems afterwards and if you don't install the bushings exactly right, you could introduce even more problems. I like the Moogs and have successfully installed quite a few sets, but not always exactly per the instructions.

The key to a successful alignment starts with:
1) having the K in the proper place, and
2) having the LBJs in the proper place
3) having the LCA pivot pins in the proper place

As to the use of the brakes during changes in turning angles, I have a different opinion.
IMO with a locked brake, this causes the the chassis to rise and fall during the turning action. This of course causes the control arms to change angles. I leave it to your imagination as to how that affects your measurements.

Finally, all your alignment angles are set for the straight ahead direction. Absolutely every change in the direction of travel are gonna change the alignment angles. Throw cornering into the mix with the suspension rising and falling, will only make the changes greater and faster. Thus you can see the importance of having the wheel being worked on, pointing dead ahead, during all adjustments and the measuring of the changes; and I'm talking about the dead ahead of the wheels, and NOT the of the steering wheel, which has to be centered after everything else is finalized. That is the last step and is very important not to forget about, especially on Chryslers.

And double finally, if you don't have floating turning plates, your other option is like @Kern Dog shows. Ok fine, but, if those plates do not float on each other to relax the suspension, then you are gonna run into problems with repeatability. So say you get a reading that needs to be changed, say you change it, then you retest it, but now the measurement is really way out there! So the question is, did you adjust too far or was the suspension not fully relaxed. You could be adjusting all afternoon chasing after the right number while the whole time, it was just those slip plates. So, if you use those, be aware of their limitations.

BTW, you cannot use the fenders for references.
You gotta use the stub-frames, and you gotta make sure that the stubs are properly located by the firewall, the aprons, and the core support, not to leave out the importance of the welded floorpans, the integral rockers, and the T-bar anchors; both front AND rear. If the aprons have broken welds at the firewall, for instance, all bets are off.

Ok so, that's all I got,
Happy HotRodding