I've had an 05 GXP trans apart and played in the 4T65E a good amount
There is no 2-3 band in there. There is a foward apply band (engages in D, 3, 2, 1) a manual 1-2 band (engaged in 1 or 2) and a reverse band that only engages in R. The forward band would be the likely candidate to be breaking. I suppose if it was breaking and not fully broken, that could exhibit some issues.
Scored pump could have been leaking a good amount of fluid etc. Maybe it was leaking worse when cold and when it heated up things expanded and took up some of the gaps.
Converter debris, this could explain a lot. If debris gets into the valve body...things can get very out of whack
