The sights are off center. I need to move the sights about 2" to the left.

On the 365XL do you just move the front sight, or is the rear sight still adjustable?

And yes other people have shot the gun and verified it is not just my shooting style.

If they are truly off center, does centering them look like it would move the POI in the proper direction?

You can move either, but if only one is off center, and centering it puts you on target with POI, move that one.

I guess my real question and concern is the rear sight. Does it move or not? I was told that the rear sight is screwed down to the sight plate. Can anyone tell me if you can loosen the screws up and move it a little, or front sight drift only?

Ah, my mistake as I didn't recognize the fact the XL was drastically different in this regard.

Actually, and I don't have an XL but I believe you are correct, the rear sight is fixed in position under the plate. If it's off center I believe that would be a manufacturing defect and you would need to contact SIG.

Your only option for windage adjustment on an XL is to drift the front sight.