After several hours of trial-and-error dis- and re-assembly, I got the cueing issue figured out. No thanks to the service manual, which basically said "We just want to talk about the ICs and transistors - if it's a mechanical issue, you're on your own." I don't have a ton of experience with turntable innards, but I think the PS-T3 has a pretty unusual design for its cueing mechanism. There's a narrow strip of metal that has a fork at one end, and is bent at the other. It moves up and down by two flat metal pieces that slip against each other, with a spring that brings them back into alignment after moving. The grease between them was dried out, causing them to stick. The forked end of the strip lifts and lowers the rod that the arm rest is attached to. There's a small screw painted with Thread-Loc near the bend, that adjusts the height of the lifter. (It was pretty much impossible to get a good grasp of the rod or to adjust the set screw holding the nylon thing, without taking everything apart including the tonearm, but I was able to wipe off some dried grease from the tip of the rod.)
Photos attached for illustration:
