The correct gauge on the stripper ALWAYS cuts through a bunch of strands....100% of the time.
It sounds like you just need to be shown the proper technique and with a little practice you'll be ok.
Don't forget there are strippers for only solid wire, and strippers for stranded.
One thing to try is to cut the center of the zip cord first,(with the cutter part of the stripper, or a knife) then strip the wire but don't squeeze down all the way.
So, you are cutting through the insulation 90% i.e.. Then re-grip it with the stripper and slide it off.