The handle that was attached to my MOEN model 1222 shower cartridge broke off. The stem of the shower cartridge broke off and was attached to the handle. I can see a short length of the stem deep down in the cartridge.

I tried pulling the cartridge out with needle nose pliers, but it won't budge. I did remove the metal key that holds the cartridge in place. The MOEN instructions say to turn the cartridge 45 degrees clockwise and then pull the cartridge out, but I can only turn the cartridge about 10 degrees even when using the plastic tool designed to turn the MOEN cartridge. Is it necessary to turn the cartridge 45 degrees in order to be able to pull it out?

Employees at a plumbing supply store I went to said that all the cartridge pulling tools they know of are designed to screw into the cartridge stem, but my stem is gone. How do I remove the cartridge? Thanks for any replies.