Success! ...But there was something else wrong, too! (and Modette, thanks for the info!)
Here's the recap and Lessons Learned...
I neglected to mention earlier that to remove the starter, you also must pull the oxygen sensor with a 22mm wrench.
A&M Motor Supply had a different brand of starter motor this morning, but it also had a copper stud for attaching the battery cable (are they all like this now?) I passed on it, afraid I'd shear the stud off like the previous starter with a copper stud, and instead decided to open up mine and see if I could find out what's really wrong. I watched a few youtube videos. So, that makes me an expert now, right?
No burnt wires inside, missing commutator segments, and the four brushes looked long enough to use. So far, so good.
Now for the bad: thick black dust (from the brushes?) covered everything. Whatever original grease was present had hardened into waxy crud. The commutator contacts were black (should be shiny copper), and black crud filled the gaps between the commutator segments.
I shot everything with a can of electrical contact cleaner, scrubbed it with a toothbrush, and dried with compressed air.
Each of the four brushes had burrs on one side, I guess in the direction that the commutator spun. I used a tiny file to remove those.
I cleaned the gunk from between the commutator segments with a piece of hacksaw blade. It was a perfect fit.
An emery board restored the blackened commutator segments to shiny copper color.
I applied some dialectic grease to the gears and other moving parts (from O'Reilly's - comes in a small dispenser can for around 8 bucks) . If any of it migrates to any electrical parts inside, it won't short it out - I hope. I used it sparingly.
Putting it back together requires some way to keep the brushes compressed while putting this assembly (part of the end cap) over the commutator. I used zip ties, then cut them off just before closing it up (it will be obvious when you get to that point).
Cleaned and lubed, the starter and solenoid functioned perfectly when connected to a battery on my work bench - encouraging!
About this time, I called Normandin Jeep, San Jose, and discovered they have a starter in stock for $168 (a new design heat shield is required for $40 more). DOH! I'd have bought one.
Convinced I had restored my starter, I installed it in reverse order: Loosely bolt the starter with the two 15mm bolts, then move to the "possum hole" in the wheel well to connect the wires. Back under the Jeep to attach the heat shield with two 10mm bolts. Tighten the two starter bolts. Reinstall the oxygen sensor. Use new Lock Tight Blue on the four 15mm drive shaft bolts.
Now, go back to the wheel well and re-attach the solenoid wire lug! Somehow, I managed to push it off while re-installing the heat shield.
Reattach plastic inner fenderwell with three new plastic rivets. Mount wheel. Reconnect the battery. Turn the key: Click click click....
Ok, this was VERY disappointing. The starter worked on my bench minutes earlier. I went back to the battery with a volt meter - 12.0 (not 12.7 a day ago). Hmm. I attached a jump start battery to it, and turned the key - the engine turned a bit, then back to clicking. The battery is now suspect again.
When this first happened, I tested the battery with a volt meter and hydrometer, and both looked good (see earlier post). This time, I pulled the battery and took it to Wal Mart, where it came from - it was still within the three year warranty period. After an hour of waiting in lines, they put it on a tester that seemed to put a load on it. A print out showed the rated cold cranking amps as 765, and the tested CCA as 330 - along with "REPLACE BATTERY". I got a replacement battery. Had to pay an additional $45 because they no longer stocked mine. Whatever.
Back in the Jeep, and it starts fine. Drove it off the ramps, attached the skid plate, and I'm done. So, was a starter refurbish really needed? I saw it "drag" when tested at A&M Motor Supply, so I think it had issues. Clearly, the battery was bad, even though a hydrometer showed it with a full charge. I guess the capacity had been reduced so that under load it would not produce the rated amps, regardless of how well the chemistry looked.
I hope this helps some one in the future.