I misread your post and thought it was the OP posting. I cant agree more about swapping one thing at a time and balance would not effect pull.
Side note. I have a 2006 Grand Caravan, put new tires on it drives straight as an arrow, after enough miles to need a rotation it pulls slightly to the right, as in drive straight at interstate speeds and let go of the steering wheel and you will drift into the next lane. rotate the tires and the pull is gone till the next rotation time. had a couple of shops look at it and none could find an issue with alignment. Left rear wheel is cambered in at the max of the spec, only odd thing.