A couple hrs later and the one-shot pump hasn't freed up at all. I tried to grasp the plunger with a pair of pliers, but there isn't enough of it exposed to grab onto. I tried suction cups designed for valve lapping, but not strong enough. Will check it again in the AM, but at this point, I'd be shocked if the ATF helped.
I just ordered a TECO E510 VFD, and some oil for the machine. Looking at fixtures to tram the head since I messed with it during transport.