They were out of patience at Home Depot.
Well I got it out. Wasn't rust. Or the very dry grease that wasn't helping. I'll explain.

This didn't work. I had a LOT of pressure on things, using my old gear puller. Necessity being the mother of invention and all.
Wouldn't budge.
I ended up using brute force. Drove some chisels between the brass jaws until I saw that the dynamic jaw moved a bit. Then a combination of driving them further in, and beating on the back end of it with a large pipe with a 2lb sledge, and a small piece of mild steel flat bar between the pipe and dynamic jaw tube as a buffer. After getting it out I wire wheeled the big pieces and that's where it got interesting. Everything looks fine, but the jaw slides in until it binds about an inch shy of sliding home. If I push it hard I have to tap it with the pipe and hammer to get it loose.
I have a feeling now that the screws on the collar were broken off when someone was trying to take them out with a lot of tension on the collar because everything was bound up.
Next I'll color it with black marker and slide it in to see where it's binding.

Made in June of '64.