TCM Changes P0733 and P0734 DTC codes?

I don't have any possible way to do all this. One, it's beyond my basic mechanic skills and Two I'm not sure if my Autel AL519 can do all that or not plus I don't have a specific pressure gauge that does 300 PSI as described. What I might be able to do is flush and blow out the cooler system which in this car is through the radiator (fins I believe) but I highly doubt there's a blockage. The reason I say I doubt there's a blockage is because when the "blowout" of the return line to the transmission happened it blew tranny fluid all over to the rear of the car, literally. The line came off the hose pipe because the clamp popped loose. The reason I'm thinking the TCM may have been damaged is previous electrical issues building up to the transmission burning out. I want to know if this model TCM requires a scan tool if I put another OEM TCM on it or do they require a reflashing? I know that Chrysler switched to the scan type but don't know what year. If I put another TCM match for the model and year OEM can I just do a simple reset and relearn without the scan tool. As mentioned, I'm not sure if the AL519 is capable of doing that reset/relearn I haven't used it much. $2,200 put in this so far $900.00 for the used transmission and $1,000 in labor getting it installed. This car isn't worth even 20% of that. All I want to do at this point is eliminate possible culprits based on known symptoms, that's all. I'm ordering a used TCM that should be here after the holiday. I can do the installation myself, no problem, as long as it doesn't pour rain or snow.

I didn't need to do all that Pinion Factor Procedure business. The TCM I put in it is an exact match right down to the alpha characters at the end (Firmware Version), it was a used one from exact same year, model vehicle as ours. TCM is functioning correctly now, the old one got damaged from electrical problem during the burnout of the transmission. As soon as my new scanner arrives, I'll run it through the software checks.

I believe your initial theory of a clogged cooler, not just the lines, is on the mark. This one is in the radiator and I'm not changing that combo, so I'll install a new auxiliary cooler which I did on my '98 Grand Caravan Sport. That solved a lot of overheating problems I was having in the Sport and pressure problems got solved too in a swapped-out transmission I had put in it after a shop put the wrong fluid in the original killing it. Hopefully this new cooler and lines will solve the problem. The transmission we had put in this car has been flush and a new torque converter put in it, so I know it's not the transmission itself. If it is it is under a 3-year warranty including the certified flush. I'll let you know in a week or so once I complete this step and scan the TCM.

The Speedometer is working correctly and TCM replacement is used from the same make and model right down to the firmware version characters on the part number.