I know that it is human nature to deny the gawdawful truth sometimes, especially when it involves large sums of moola.
You have exhausted more avenues of correction than the average Joe. If you are REALLY going to install a USED unit, then bless you. I do not know how much difference the cost of that used one is from the cost of a Jasper unit, heck, I do not even know IF Jasper even HAS one or will rebuild your unit.
"Under a thousand dollars"... "It ran when it was parked"... cute catch phrases to part you with more money that simply stating that it is used, germane to it's TRUE used value.
YES you DO have to reprogram the TCM. Period. That is the least of your problem.
Are you planning the R&R operation to be done by yourself? If so, have you considered replacing, as opposed to flushing the cooler?
As an Automatic Transmission Specialist, I CAN tell you rather accurately, that flushing is Russian Roulette.... plain and simple. Debris can get packed into nooks and crannies of the cooler, and then get dislodged later, only to decimate your expensive efforts.
When I repair automatic transmissions these days, when the cooler is part of the radiator, ALL of the units I either replace or rebuild get a new radiator. I tell the customer that they are killing 2 birds with one stone in that the cooling system is also being brought up to snuff; optimal function.
The external type cooler is a no-brainer.