Something I have noticed over the years is that most factory string don't have near the twists in them that they should have. This in itself leads to instability. You have all those strands acting individually. Twisting the string up so there is at least one complete turn per 2" of string length helps tighten the bundle so the strands work as a unit better.

This will have some side effects. Depending on how the string was made it'll take a while for the strands to stretch so they are all the same length. Then it should stabilize. Twisting makes the string smaller in diameter so serving will get loose and slide or separate. Then you have to reserve everything. This also shortens the draw length so you may have to twist the cable up accordingly to maintain draw length and then readjust the weight.

I used to conform to the idea of "training the string". That's moving strands around till the peep roills to the right position all the time, but...........

The best answer is a good set of aftermarket strings that are made properly in the first place. Gibblet on this site makes some very high quality strings and at a reasonable price. Pick your colors and should you have any issues his customer service is outstanding, too. Do this and I'd almost guarantee that peep rotation problems dissolve. Your bow will stay in tune much longer, too.