You're doing the correct things to get that agitator off, it's on the block just as you thought. The cap is (normally) the only thing holding it down. You might try soaking it with the Liq. Wrench for a while, then agitating a big load to help loosen it. Watch it carefully though, you don't want it to come loose and damage the agitator while moving.
The spin issue you're having sounds like either a belt problem, or possibly a clutch issue. I'd start with a new belt and go from there. Belt guide says 8L330 for that model.
Good luck!!