My method with wines, which are still, is to rack to a new carboy (off the yeast et al), stablize and sweeten at the same time and let sit for a week. Check Gravity before and after week. If gravity has changed, then fermentation is going on, and more agressive methods might be needed, if not, rack to keg. (well my case, bottle).
I'd suggest if you are ok with sulfates, that you use 1 campden tablet with that along with the potasium sorbate. both Meta-k and k-sorbate don't kill live yeast, they both inhibit further growth. One prevents reproduction adnI forget what the other does. Also cooling to help drop the yeast and pectin to help clear haze (which will help drop yeast) The goal being to clear as much yeast as possible, because the yeast can over power the stablizers