T&S pre-rinse faucet leak repair

[JenMarrs]

I am trying to repair a non-check cartridge with a badly worn seat washer.
I suspect the valve seat is damaged at this point, because replacing the seat washer did not stop the leak. I think I have two choices: resurface the seat with a cutter or replace the cartridge body.
However, the cartridge is seized in the the fixture. T&S are straight pull, but I just could not break it free due to access problems and not knowing the tricks and tools.

Any advice?

I am a mechanical engineer but not a plumber. I am doing this at an animal hospital type setting where I volunteer.

 

[Smooky]

I loosen the bonnet nut with the handle still attached to the stem. Then use the handle to wiggle and pull the removable insert up out of the faucet body. There is also a bottom gasket on the bottom of the removable insert that can cause it to leak. ....If you are replacing the hot or the cold stems I would install stems with a spring check.

 

[Sponsor]

 

[JenMarrs]

Thanks for your response!
I did try removal with the handle still on, but no luck.
This is the valve that directs to the faucet vs. sprayer. Luckily the hot/cold valves are ok at this time.

What is interesting is I did a temporary fix by placing a round shim under the worn seat washer. The old washer isn't flat, which threw me for a loop. It is thick under the screw head and then steps down. When I installed the shim and tightened the screw, it caused the thicker area to bulge out. This fixed the leak but I need to understand why the flat seat washer replacement did not work.