I had been told that it was all but impossible to change the order of inventors, specifically changing the first named inventor. So, I talked to an examiner at the USPTO and asked them how to do it.
The answer was to file a petition under 37 CFR 1.182, a petition for questions not specifically provided for. The examiner said that these petitions are typically granted and that no cause has to be shown to change the order of inventors. The cost is $400.
Just don’t tell your second named inventors, as you may be filing a bunch of these.