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I would rebuild yours if possible.
There are people that "rebuild" that just throw in clutches and a shift kit and there are people that rebuild that inspect everything and do it right. Watch the 4l60/700 videos that Precision transmission does on YouTube. This man knows transmissions. The only problem is he does not do take outs. He is in Amarillo. If you want to know what your transmission is about, this is the guy to watch.
If you have all forward gears plus converter lockup and shifts are fairly firm then it is likely a control issue. Tv cable not adjusted properly. Valve body issue or governor issue. Also to get the oil out of the cooling system use some dawn dishwater soap and keep flushing until all residue is gone. You may have to replace all rubber hoses as you won’t be able to get the oil out of them and they will end up getting soft and blowing out.
The TV cable is about $20 bucks from most parts stores. Regardless if it self-adjusts, it sounds like you have other issues. Is this shop a transmission specialty shop? What exactly did they do? Is your truck an R-10 or a V-10? O'Reilly CA1970 or Napa ATP 17909 should work
So they'll put a new TV cable in and if it's not right, what are you going to do?