I got a lot out of this thread, so I joined up here to post some results. Thanks to everyone who has contributed here.
First, I just got a Sony D-35 from eBay that was "untested due to lack of power supply." I took this to be eBay-ese for "doesn't work right, but I don't want to say that so I can charge more for it." I was not disappointed. It read a disc OK, but then skipped most of the way through track 1, halfway through track 2, and landed somewhere in track 3 before settling down a bit. Figuring it might need adjustment, I opened the back and looked for the 50x trimmers that are so ubiquitous on old Sony players. Adjusting most of these made things not much better to far worse, so I returned them to the spot where the player seemed least unhappy.
I then noticed that it worked better on its side. Not just better, in fact, but MUCH better. It could play track 1, the transport was much quieter, the CD I was testing with didn't suck as much... you get the idea. (Kidding. It's actually a great disc.) So this made me wonder if maybe the problem was more mechanical in nature. The motor didn't seem to have bearing issues or runout, but just in case, I opened the lid and wedged something into the lid sensor switch cavity. These old players kind of rely on the magnetic clamp to keep the CD and spindle tightly coupled, but it was still able to slip up to speed eventually, and then it started playing with no issues.
I took the lid off its hinges, removed the metal plate on the inside of the lid (losing one of the impossibly small screws in the process), and noticed the metal plate had a bit of a bow to it. Kind of like somebody sat on the poor thing by accident and bent the lid slightly out of shape. So, I worked on that for a little while, trying to coax it back into flat-ish. The plate has all the electronics for the display and buttons attached, and serves as the retainer for the disc clamp. It's also on its own hinges, so you can close it over the disc while the cosmetic lid itself is still wide open. You still have to trip the lid sensor manually, though. While not perfect, the transport was able to play the disc much easier now. Pressing buttons, or moving it just so, would still cause a little bit of friction on the disc, and so more skipping. But it was much improved, so I kept working on reshaping the plate. I found a dip on the back by the hinges that I missed before. I wasn't able to flatten it completely, but I did bend it back enough that, when reassembled, it seemed to be working pretty much perfectly.
I put in another disc to test with, and listened to the whole thing without issue. Looks like this one's back in service.
Now, I have two D-88s that are both very ill. At least one of them appears to be having trouble moving the sled around. It will attempt to crawl by a tiny, tiny amount -- but it's s-l-o-w moving, and gives up almost immediately. You can only tell by watching the motor gear teeth. It turns about 1/4 turn and stops. I've noticed that if you position the sled somewhere by hand, it will sometimes just start playing whatever happens to be over the laser, but it can't seem to track anywhere by itself. I haven't gotten as far with the other one, but it similarly has trouble getting even a TOC. Both seem to be missing a channel on the headphone output. Probably about time for new electrolytics all the way around, and then who knows what.
And then there's the D-5. It's working just swimmingly, aside from smelling like someone left it in a moldy box for 15 years. Sony did not mess around with that one. Thing's built like a tank!
