Agree that it is not the wheels/tires that're affecting your caster.
First thing first, I'd go get your new wheels/tires balanced since it sounds like they wouldn't even do that. Just to make sure that the wheels aren't out of round or anything crazy - in which case you'd have to send them back anyways, though they still wouldn't be the cause of your alignment issues.
I'm not very familiar with 4Runner suspension yet, but to give it to you basically - caster refers to the relationship between the upper and lower steering mounts that the tire is attached to. In this case, you've got the upper and lower arms attached to the steering knuckle. For positive caster, you need the upper arm mount to be further towards the back of the vehicle relative to the lower arm mount. So if you're not able to get enough caster, that means that either the lower arm is bent backwards (reducing the distance from the lower to upper), or the upper arm is bent forwards (same effect).
Anyways, maybe you could start there for some ideas. Caster is very easy to mess up after a wreck (even a minor one) because these parts can get slightly bent and if the tech isn't looking for it, you won't see it. However, caster usually doesn't affect tire wear nearly as much as out-of-spec camber or toe, so things could be worse.