...don't lose those little screws!
Removing the cross-recess screws and putting them aside in a jar was the easiest part of the restoration!
The face plate did. not. want. to. come. out. Holding the ratchet by the handle, with the entire ratchet inside a ziploc bag, I was pounding it on the edge of my workbench just under the head, to try to pop it out, but it would only budge at the top a hair, and not enough to get something under it to pry it.
A lightbulb went on over my head and I grabbed a Waldes-Truarc snap ring plier 1340. Stuck the ends in the screw holes, squeezed hard, and pulled, and managed to get it looser. Then I put it back in the bag and pounded again a few times and it popped out.
Turns out the bag was unnecessary. The batman pawl is connected to the switch, which is pinned. The pawl does not come out. So the spring and ball have no way of flying anywhere.
Thankfully, nothing is worn or damaged or broken, it was just gunked up with hard cosmolene and rust.
I soaked the ratchet, the face plate, and the gear in SG for 15 minutes...
...then in Evaporust for 15 minutes (fearful of losing the black oxide finish), wiped it down with WD40, and it was looking much, much better.
Next I lubed it up liberally with Hoppe's gun grease...
...and re-assembled and it is working like new again!

And has a nice new cozy and cuddly retirement home with black oxide kin in this set.

Thanks
@jabberwoki !