Tires and wheels do not change your caster, they create a need to change caster.
You're going to listen to whatever that tech spews out, so it really doesn't matter what we say when it comes to not going with cam bolts. An at home alignment as far as caster is concerned is crazy easy. All you need is an angle finder (preferably digital to make it easier), the ability to change lengths of control arms, and a flat surface.
If it has been happening since you bought the jeep, and there wasn't a lift on it when you bought it, I would say that the caster rabbit hole isn't going to fix your issue. Unless the control arms are screwed up, or it was very poorly aligned from a previous owner, there shouldn't have been caster issues then. Have you had anyone check if the axle is bent?