I had a shower unit (brass) that was seized I tried to use the plastic cap sold with replacement cartridge but it was not strong enough I had to remove both clip the horse shoe and the round clip inside then remove inside stem of cartridge. Then use a #6 screw extractor with a lot! Of force to free it up good luck.
I had to do this on 2 shower units 27 years old

You piggy backed onto a two year old thread so I gave you your own. You describe a Moen valve. Moen makes a cartridge puller for those stubborn cartridges,(see image) so you don't have to go through the hassle of removing the stem. Thanks for your input, Tom