@mannebk You have gotten very good advice of 1) get a scanner on it and see what the computer (ECM) is seeing and doing. 2) Turn it TF around and drive the 2 hours back to a KNOWN GOOD RECOMMENDED SHOP esp. with your bitching about BAD techs/shops out there. Better yet where is your final destination your tail is on fire to push this malfunctioning rig to? Maybe a shop recommendation there will work esp. for warranty if needed.
Go ahead and waste your time and money rebuilding the trans. The rebuild can last exactly 30 seconds slipping before it burns a clutch pack up from slipping if you don't catch the problem. New parts don't mean good parts so if you introduce a second problem it gets more fun.
One of two things you will see on the scanner: Gear Commanded and Gear Selected. Also input and output RPM. If the gear commanded and gear selected is neutral you know the shifter is out of adjustment or the electronic switch on the side of the transmission (if equipped) is shot. If it's Gear Selected OD and Gear Commanded N (or 3) likely it's slipping the TCC or 4th Gear and MPH is too high to drop into 3rd. You need to know if something is slipping or if it's an electronic wiring etc. problem. Major info is any codes indicating a wiring problem or slipping.
The Overrun clutch for manual 3rd is a weak point. Doesn't take much to burn it up. You are taking the grades too fast and/or too heavy if you burn the brakes up. Other braking techniques may need work. Weigh the rig and make sure you are not overloaded. This transmission and a low compression 454 are Dog S! useless for compression braking anyway. Don't count on it: I couldn't as the weak manual 3rd overrun clutch was one of the first things I would burn up in a 4L80E towing the grades around here. (Then drive the trans with that burnt clutch 50K miles till the TCC started slipping and rebuild time.)
@GenBiltstein kinda sugar coated it but his advice is accurate. Couple things a good shop can do is apply "updates" to the transmission like more lube oil to some places. Also if you have say a rare cracked case leaking oil pressure the trans shop can find it.
60K miles at full weight... Even Grandpa going to church on Sunday has to get it close to the speed limit. The transmission, engine, etc. shown by single digit MPG is working harder than an unloaded pickup or Suburban. It may be low miles but it's hard miles. I was only getting 50K out of this transmission between rebuilds. Mainly the weak TCC slipping brought it in. Last one I fixed by simply dropping a Yank performance triple disc converter in.
One last thing: work on the rig when the exhaust is cold or header wrap the pipe in the area you plan on working on. Wrap would keep radiated heat to the trans down at least.