If I can't disassemble the wiper pivots, I want to soak them in something that will
penetrate up the shaft and dissolve any and all old lube/crap.

The solvent cannot be corrosive.

I can submerge the wiper parts in a bucket of whatever for a week or two if that's what it takes.

What kind of solvent should I use ?

Soak them in a can of carb cleaner.

The pivot housing is aluminum, after a week carb cleaner would eat it for lunch.

Mineral Spirits and then use the grease kit to clear it out after it dries.

Grease kit ?

Mine were very close to frozen, I needed them to work before drag week last year so I took the arms off and ran some 3n1 oil down the shafts and turned the motor on. It took about 5 minutes but it limbered up nicely and they worked nice and smooth. It was a good thing I did that because I used them for hours and hours that week!

I like the idea of installing a zerk fitting, but to drill the housing for the fitting, the shaft has to come out.
This is what I can't figure out, getting the serrated cap off to pull out the shaft.

What I have done on my restorations is remove them and soak them in naphtha or mineral spirits in my parts washer and move then around. It will loosen up the old grease. You can squirt some brake cleaner type solvent in there to help things as well. Lots of movement and some air pressure will help. I drill a hole in the middle and insert a grease zert as well. There are several kits on the market with seals. Once it it as clean as possible with solvent and air pressure, I grease it up and it’s good for another 40 years.

OK, for those interested, I used Kano Kroil on both ends of the assembly. Several applications.
It loosened up quite nicely, no disassembly needed, although, not being grease, I don't know how long this will last.

Just drill it, they can be done while assembled. They are so smooth when filled with grease. Can’t hardly leak water either. Did this to my 20 year daily driver and all is well.