check the control handle travel pot also...

on the ray/cat trucks they did this and generally the pot was going bad and caused the truck to move erratically, anything from creeping when the handle was in neutral to erratic travel movement and even as you said, actually moving in the wrong direction when activated.
Usually a relearn of the control handle fixed it but ultimately in the end the pot had to be replaced and calibrated/learned.

and as you said this also can cause it to be very difficult to get the truck into maint mode to do the learn, it can be done but you will have to keep moving the handle and holding it in different positions till it likes what it sees to allow you to enter maint mode. Using a vom and monitoring the signal might be helpful in achieving the desired voltage range for neutral till you get into the maint menu.