Car mechanics have some kind of solution in which they soak things like this for days. I would even consider putting some in a stainless pot and heating it up carefully, after a day or two of soaking. Then remove the assembly from the liquid and put it in a Ziploc bag and freeze it for a couple of days. Repeat as needed.
How about this?
"A scientific principle reduces the surface tension so that this amazing solvent creeps into openings as small as one millionth of an inch. Kroil loosens frozen metal joints in minutes. Dissolves gum, dried grease, and oil -- without attacking the metal. Displaces water, provides lubrication and prevents rust."
When you are ready, put the shaft back in the vise, and use a propane torch to heat the circular part carefully near the shaft.
To paraphrase a famous old carpenter, "Give shot pipe wrench," and voila! [RIP RG Sr.]
No? Then you are shafted!