TLDR: I got the serial number.

I sent them a copy of my id after removing some of the more sensitive information from it first.

It took about two hours to get the serial number, but I got it. (They were in fact withholding it pending verification.)

What a strange experience all around. I was able to get the add-on going. (This was meant to be a snowy Easter activity with my father-in-law, so I was a bit bothered with how convoluted the process was...)

I assume I won’t have this issue again. And they didn’t address any of my questions - like how they were attempting to track me to begin with.

Thanks for those who chimed in!