If it’s not making the 2-3 shift once it’s warmed up, why do they say no problem?? Seems to me that’s a pretty obvious concern.
With the engine cold, pull on the kickdown cable a few times. Pull it enough times you have a good idea of what it feels like. Next time it acts funny, pull the cable again, see if it feels differently. Maybe the cable is binding when it gets hot?
Inspect the vacuum modulator line, especially the rubber hose connections, and anyplace it’s near the exhaust. Maybe the hose is partially collapsing when it gets hot, restricting the vacuum signal?
Replace the vaccum modulator. I think the part number is MV100 at autozone, about 20 bucks. If I’m right on the part number, that one will be adjustable. You can move shift points 2-4 mph. Put it in the truck as is, see what happens. If it solves your problem then play around with shift points. Don’t turn the screw more than 4 turns either direction!!
It could also be a valve sticking in the valve body once it gets hot. If the shop flat out refuses to help anymore, you might try dropping the pan, and loosening all the valve body bolts, then retorquing them to 120 INCH POUNDS (not foot pounds!!) starting in the center and spiraling out.
If you still have the issue after all that, it’s time to remove the valve body. It’s pretty easy on a TH350, just messy especially if the trans has no drain plug.