If it stays in 2nd, it's a possible control/kickdown/governor/VB problem, i.e. the 2nd gear servo is staying on. If it goes into a false neutral and freewheels instead of going into high, then it's the front clutch not applying. But, since reverse is also not right, you are correct that the high clutch is the common element. Multiple things going on. A pressure check of different functions would help. Or as suggested, swapping in a known good VB would confirm or rule out all of the issues being valve body related. Band adjustments also need to be verified.