Unfortunately the only way to add a document outside of an initial application or renewal is via an enrollment center. When Mrs. Majuki became a US citizen, I did my homework to see if there was a way other than going to an enrollment center. There wasn't.

The information in the Secure Flight fields compares to what's on file for Global Entry. Is there is not an EXACT match, the system will kick it out and you won't get Precheck (other than if you're part of managed inclusion, ie random Precheck). Your data points don't really lend themselves to meaningful conclusions because they're across different airlines. It is also possible that the system had been kicking out your name but you were more likely to get random Precheck on a domestic versus international flight.

You need to double, triple, and quadruple check that the Secure Flight fields match your trusted traveler profile. For instance, the name in my profile is First Middle Last. I've had some travel agents pass along FirstMiddle <null> Last in the Secure Flight information, meaning the system was looking for someone with a first name of FirstMiddle, no middle name, and a last name of Last. The ticketing agent was able to fix the data, check me in again, and this restored Precheck. Make certain that your middle name with the space is in the middle name of the Secure Flight data if this is how it is represented on your TTP profile.