American Standard Ultramix - Stuck Balancing Spool

After moving in to my recently purchased older condo, I found that one of the showers doesn't work. The valve (an American Standard Ultramix) only outputs cold water. However, I know that hot water does get to the valve. The shower has not been used by the previous owner for years.

I replaced the cartridge and both stop valves. The only original part left is the balancing spool, which is completely stuck. After lots of struggle, I managed to remove the cap but the spool won't come out (second pic is after removing the cap). I had a plumber come over. He seriously injured his hand trying to get the spool out and then gave up. I need help...

Option 1: Find a way to remove the balancing spool. Tried soaking it in vinegar, WD40, pulling with various tools. Not having much hope here.

Option 2: Replace the whole valve. There is no access from the back wall. I really don't want to redo the entire shower. Is there a trick with which a few tiles around the valve could be cut out intact and put back in the clean way after the valve is replaced? As you can see in the photo, the valve is quite wide due to the stops.

Would really appreciate any help or thoughts.

 

From this point they should come out with the use of easy-outs. Also Delta has the identical spool assembly which is cheaper than American Standard.