You also mentioned looking at the waveform of the cam & crank on a scope. Here's a video on testing the cam sensor on an 02 (which will be pretty similar to your 03). I skipped ahead to where I used a cheap scope to verify the waveform of the cam sensor while running. You can do the exact same thing on the crank sensor. In a perfect world I'd have a dual input scope so you can see the signals relative phase. Which really only helps if we know how they need to be...which is on my list of things to figure out one day.
Somewhat related to this, since I mentioned it in my post above about the flexplate...
Since you swapped from an 03 to an 03 it might not be a thing, but the flexplate acts as a tone ring for the crank sensor. Earlier TJ's had window pattern that could tell the computer where it was in the cycle. The later ones didn't have that, but instead had a timing learn process that I really don't know much about. The cam sensor is similar, but I don't believe it changed other than when they went from dizzy to opda.
From a 97-02, which, perhaps not coincidentally, is for a 32RH. The 03 & 04 is extremely similar in function, but must be slightly different for the 42RLE.
This is from an 05-06, which corresponds to the 42RLE.
I know even less about manual transmission than I do about automatics, but my understanding is they function similarly. So... is it possible you have the wrong flywheel or flexplate? And then is it necessary to "time" them to the crank? I don't know since I've never had a flexplate off an engine before. I mean, the answer is YES, it must be timed, but maybe the bolt pattern enforces the correct timing or maybe there is a process. I wouldn't even bring it up except that you've tried a bunch and we've kinda zeroed in on timing as the culprit.