Bullets not seated the same depth can cause vertical stringing and the other is the rest that (bag) is soft. Bench rest shooters are your example here,, Use a Hard or fully packed bag on the front rest. Shifting sand bags will cause you problems.
For checking accuracy it is best to have the butt on a rest as well.

FWIW With my grip hand, it never leaves the pistol when shooting for accuracy test. Revolvers are easier than the Contender but still possible.

Have you tried backing down off that charge? Don't understand the reason for that high of charge with Lil Gun and would ask consideration of using 4227 for a real accurate load. Even if you dropped down to 1400 FPS, that would get the job done for most things.