Update:
The main surgery is done. The patient survived.
It turned out to be less complicated than I thought it was going to be. Basically, the center shaft for the automatic gear assembly was full of gunk that needed to be cleaned out. The gunk was holding the gear up just enough that it would stay put when the autotrip engaged, so the autptrip was working but it would relatch itself before the gear could move.
Once it was cleaned up, the gear turned freely enough for everything to turn when the autotrip engaged. Thus, we now have a LAB 80 that's (mostly) fully working!
Mostly. I'll come back to that.
Here's the basics on my process:
To get the shaft out, I had to first take off the platter and undo the nut holding the top of the center shaft in place. Everything else happens on the bottom so tuen I glipped over the deck.
Next I removed the spring attached to the arm that engages the mute switch. Then I removed the housing over the RCA terminal output (remove the clip holding it to the standoff with needle nosed pliers, pull the housing out over the standoff, unhook from the metal at the lower corner.)
Next the triangular bracket at the top of the gear assembly had to come out. I removed the clip onnthe remaining standoff, unscrewed the other standoff (this one has a ling screw running through a loose standoff so I set that whole assembly aside) and undid the nut on the other side of the center shaft.
From here I removed the pot metal part that engages the autochanger. This was very gummed up so it took a little doing to get it out, but it did come out.
Next I removed the center shaft itself, keeping the main gear in position. There was a captive washer on the other side of the main gear, so I took care to make sure it stayed in place underneath the gear (it didn't stay.) The spring tension on the main follower did pull the gear a little bit out of position, but this wasn't too big of a deal.
Next I cleaned the shaft, inside of the gear, and inside of the autichanger piece with a spray degreaser (Remmington gun cleaner) and a cloth / Q-tips. Regreased with a light machine oil (Remmington gun oil, which I find works well in these sorts of applications.)
Then I reassembled basically in the reverse order.
That captive washer was a little bit of a pain, but I was able to reposition it with a dental pick, follow through with a screwdriver to get it all lined up while I held the gear in position, then reinstert the center shaft. The pot metal autochnager part has to be keyed with a peg so I kade sure that was positioned correctly, then it was basic reassembly making sure all of the washers were where they were supposed to go.
Overall it was a 20 minute process. I took pictures along the way, which helped.
So now the deck is mostly working with a handful of caveats.
Firstly, the positioning of the tonearm after a record drops isn't fully consistent. sometimes it drops a little ways into the record. I assume that this is something getting gummed up.
Second, as user loudnoises alluded to for my Miracord, this deck needs new foam in the suspension. Even the slightest footfall will cause the record to skip.
Third, the base is sagging after 60 years of having a heavy turntable mech sitting in it. this doesn't seem to be impacting anything but is worth noting.
Finally, something went off with the wow and flutter during this whole operation. I probably touched the inner rim of the platter with my greasy mitts at some point, so I'll have to look at that. Or maybe it'll sort itself out after a couple hours of play, who knows.
For the moment, I consider that good enough to stand in for the Miracord. It's more or less doing what it's supposed to, so it'll be getting some work for now.