Stuck diverter valve

I have an old Kohler shower diverter valve that is stuck. After removing the bonnet nut I found what looks to be a floating sleeve holding the diverter valve in. Any suggestions how to free up the sleeve without damaging the stem or housing? Could I just unscrew it part way and give it a few good wacks into the valve to loosen it or will this damage something? I have removed the hot and cold water compression valves with no problem.

I can't tell what I'm looking at in that pic... could you back up a little so I can see more? Don't have a clue what I'm looking at.

Got it out

Well I did manage to get it out by brute force. Pushed up and down and side to side on the handle until I broke it loose. Looks like hard water deposits were the cause. Attached is a picture of what it looks like. There is no gasket any where on it. I hope the gasket does not go on the very end of the stem. There is no screw there just a rusty nub.