Does anyone have any tips/tricks on how to remove the hot water handle from it's stem?

I've tried liquid wrench penetrating oil (I applied many applications) and a handle puller (it just kept sliding off as I tightened it).

The company is Harvey Machine, Co. I'm pretty certain it's the original faucet & handles. The house was built in 1952.

Is it time to call it quits and bring a professional in?