Looking for ideas to free this adjuster up.
I've been soaking it with kroil for several weeks.
 

Very common. I put it in a vise with a piece of inner tube to protect it and use a 1/4" impact driver.

The nylon spiral looks cracked.

Hmm... at first glance it looks like someone modified it?

Nevermind.  I had it upside down in my head. 

71DT250, have you replaced the spiral ? and did you use brass ?

Yes I have the KDI brass spiral on 2 of mine. Very good solution. Should last another 50 years. Follow the directions. You have only 1 chance to get the orientation correct. Use a vise to press it straight on. I used a small file to taper the edges slightly. And use white lithium grease.

You can make sure it fits before installing it on the actuator by inserting the brass piece into the sprocket cover.

Clarify: I don't grease the brass piece while installing it on the actuator. Grease it when you put the assembly into the sprocket cover.

The tight nut isn't something oil will free--its just locked up tight as nuts do & not rusted. Its tight against the steel center not the nylon. I just try to hold the cable arm as best as can with vice grips & heave ho. Don't go trying to hold anywhere else or it'll squash it.
Better idea--Might be easier to grab the nut in the vice so its held steady, then with your vicies or good pliers on the cable arm, just crack it free. Go the right way though.