I provided the PNs above, you could have gone to Rock Auto or any online GM/Allison parts house and ordered them.
I've never "relearned" an NSBU. It's outputs are not coded in any manner that needs to be learned, if you installed it with the gear selector in neutral as they indicate it shouldn't be an issue and may only take minor adjustment beyond that.
When installing a new NSBU, the dash indicator doesn't matter. Physically put the transmission in neutral (2 clicks rearward from the fully forward position). You are installing THE part that will tell the dash where the trans is physically placed with the gear selector.
No clue on your stamping questions.
I do not know the wiring difference between the 4L60/4L80 NSBU and the Allison, I've never installed the wrong one with matching pigtail.
What do you mean by "why didn't it throw it into limp mode?", meaning why didn't it lock into 3rd gear? The truck had zero idea what gear it was in thus getting odd readings. Once you unplugged the trans it went into a mechanically locked 3rd gear, meaning with all solenoids deenergized you will hydraulically have 3rd and reverse.
The truck won't default to third gear just because it doesn't understand the NSBU reading. Usually they say range shift inhibited or similar for NSBU issues, or they simply won't start.