I'm not claiming victory yet, as I've only had 2 overnight cold start attempts, and it's been about 80F in the mornings (about 4 to 6 degrees F hotter than when I was testing). But I replaced my original TPS with a new OEM TPS this weekend, and reset my throttle stop screw correctly. Not only did it improve my idle shake, but the 2 cold starts I've tried have been instant. I'll update if I see things getting worse or going back to the original problem, but I'm a bit dumbfounded that the TPS would have caused this issue for cold starts.

It's interesting to note though, that my original TPS did adjust properly, and was in spec per the FSM. My only indicator was a code 7, and I was able to see bad voltage at the ECU side for VTA (it would never change and wasn't in the range). With the old TPS still on there, jiggling the connector and wires caused the voltage to go back in spec. So I was wary that the new TPS was the problem, and I'd still have to replace the wiring. I'm still thinking I may have gotten lucky when putting the new TPS on and the connector is just in the right place. But I do know that when I was getting good voltage at the ECU after jiggling the connector on the old TPS, I was *still* having my delayed cold start issue. This seems to still point the actual old TPS itself, and not the connector or wiring.

tldr; Replacing the TPS (which was functionally sound per Ohmmeter) seems to have fixed the issue for my delayed cold start, and improved my warm idle shakes (separate thread).