We almost exclusively fish slip corks and never have the issue you are describing. On my wife and my poles we use power pro original 15 lb braid or gamma 15 lb. The gamma is very difficult to move the stop knot on. In fact it's almost too tight. We use the pink string stops and I tighten the crap out of them with a pliers on one end while holding the other in my teeth. I melt the excess off with a Berkeley line cutter right to the knot so there isn't any excess , this creates a football shaped stop knot. On my daughters rod I use 6 lb hi vis mr crappie line simply because she could easily get cut by the braid. I use the same bobber stop and tighten and cut it the same way. It holds very well and never slips.
The stop knots we use come in a 100 pack tube from grizzly jig, but I forgot who the manufacturer is. We use the bobbers the same company who makes the stopers does which are called crappie stalker. They come in green and pink. We use a glass bead Instead of the bead that comes with the stoppers, I got them at cabelas and think they are a 4 mm bead.
I do wet the stop knot with some spit before I cinch it down too.
Hope this helps!