1744 is a mechanically bad TCC stuck off code. (Not a standard OBD-II Code but proprietary, and those sometimes get reported wrong. My source for definition is a FORD manual.) Now the fact it is throwing that code MAY mean your TCC is stuck off, or it may mean there's a bad input fooling your PCM somewhere into thinking it is. You claim you have TCC lockup occurring normally, so I will accept that - but want to ask, did you use the same TC when you swapped trannies?
This is one where a breakout box and a transmission tester would really be helpful. Of all the transmission pinpoint tests, TCC may be the most extensive. (Pinpoint test C) It involves testing the cables to the PCM using the breakout box, and the transmission itself using the transmission tester. Your case would also call for pinpoint test J and M. One of those requires a New Generation Star Tester (NGS). That tests the TSS and OSS sensors.
Let's see what we "might" rule out. You swapped trannies and got the same code. So we know your internal harness, tcc solenoid etc is not to blame, or why did it do it with both trannies - unlikely they were both bad somehow - in EXACTLY the same way! (Don't bet on that!) I am uncertain how the computer derives a mechanically bad TCC unless it is relying on the output shaft speed sensor (OSS) and turbine shaft speed sensor (TSS) sensors (or something else) to see that the lockup is in fact occurring and in your case somehow fails to see that. However a bad sensor in those areas "ought" to show up with some other sensor related code. Puzzling.
I'll work on it a little, but I admit I am a little perplexed myself on this one. I'm guessing sensor somewhere somehow first, then cabling to the PCM 2nd.
ps. You just "happened" to have a 5R55E laying around? (swoon)