Can an alignment fix my rubbing issue?

The rubbing is pretty bad when I'm coming down from certain parking lots. By "fix the caster" do you mean move it further positive and just cut even more than was suggested above?

 

I would go w/ one of the recommendations, go to a 4x4 specific alignment shop first. If it is still rubbing, be prepared to trim. You shouldn't need a BMC.

 

My amateur view after seeing minimal adjustment on passenger side only and neutral on driver, is that some toe adjustment was made and not much else. I think this because camber moved only slightly and stayed within range. Caster could not be increased forward as it would push your wheels forward and rub more. That's probably why driver side was left behind, out of spec range.

Again, I am not a pro, but the 4x4 shop aligns with a view to fitting oversize tires, not necessarily a book alignment. They usually cut to fit first, like I did, and align after, maximizing available caster that still allows for straight cambers and toes. If you are adamant about not cutting, an upper control arm with additional caster angle, might allow a slight backwards caster cam adjustment since you already have the bmc. Again, just an amateur first take.
On my 2016, I had to cut for hours over a couple days, to get my 305/70r16, -19 offset wheels, to clear front and back of fender, beyond the bmc and pinch weld pound. Here is the rear cam.

 

I appreciate your input. I think you are correct in that they really did not adjust much besides my messed up toe.

I’m definitely not against cutting. I actually already started to cut at the corner of the bumper where I took a photo of earlier in this thread.

I started this thread asking if I could move my caster more negative for the rubbing but I’m coming out feeling like I should get another alignment with a more positive caster and cut to make it work.