It's not possible GSX would cause stuttering AFTER Pushback because, at that time, is not doing anything. If GSX really caused issues with stuttering or fps, you should have noticed them way before the end of pushback, that is while GSX was doing something.
I can’t see anything on the forum covering this type of problem
That would be already an indication something like this never happens and, in fact, nobody reported it before. Could be you tried to taxi too early, BEFORE seeing the "Have a good flight" message from GSX ?
