I've been using my 92 to get to work this week while the DD was laid up for a starter replacement, and I'm fighting a very similar issue:
At first cold start, will not shift out of 1st. Once the engine(or is it the trans?) gets a little heat into it, it'll make that shift, and once it manages it once it shifts perfectly fine until the next cold start.
I checked fluid level (good), and readjusted TV cable, no help. Decided that TPS was probably original (or at least 20 years old), and decided to take a $45 punt on a Duralast unit at Autozone.
With the new sensor, time to first successful 1-2 shift decreased a bit, so I was thinking maybe the computer was still "relearning" the new sensor (have not had time to do a battery cable pull to fully reset the ECU), but it's still doing it and I am still concerned.
I will say there have been other improvements: prior to the new sensor, I'd been dropping the shifter from D to 3 for long uphill climbs, as the truck would not maintain speed (and my MPG is a bit off, even for pushing 31-inch MT/Rs on 3:55 diffs). Now, after the new sensor and confirming the TV adjustment is right, I don't have to do that any more. Only filled up once since the sensor swap, may have seen a 1-point improvement but not really enough data on that yet.
Thinking back, I've been having this issue for maybe about a year now (less noticeable/faster recovery on warm/hot days), which may put the start shortly after the last change of ATF (due to a weeping pan seal). Didn't do it myself, and the mechanic used "synthetic" fluid, presumably just a drain/fill since he was just dropping the pan to make sure it was straight to stop the leaking. So, I'm thinking I've got a mix of traditional Dex/Mercon and whatever synthetic fluid the mechanic used, and from reading some older threads around here it sounds like it's not entirely impossible for the synthetic ATF (unknown exactly what type he used, I may try and find the shop invoice to see if he listed the specific stuff) to be a contributing factor. As I have a couple gallons of regular Dex/Merc fluid on hand, I may try doing a drain/refill myself with that after testing the new TPS and checking the two TCM harness connectors by the firewall.
I'll do my best to remember to post any updates.