The skip shift sensor will force you to shift from 1st to 4th under light/moderate acceleration. You can get an aftermarket sensor that eliminates this feature. There is also a reverse lockout sensor as well. I suspect there may be an issue with your reverse lockout sensor. Here is a link to a thread for a member that may have installed the aftermarket skip shift sensor in the reverse lockout sensor. I like your work around of shutting down in reverse.
https://www.camaro6.com/forums/showthread.php?t=543926