Did you get confirmation from an agent that it was due to a (in)SecureFlight discrepancy? If you were on the real NFL, the check-in process at the airport would be quite a bit more convoluted and complex than just an agent looking at your DL and spitting out a boarding pass.

Could it be your ticket is out of sync? I've had that happen before and in every case, it was my ticket being out of sync.

If you've eliminated the ticket sync issue (you can call in advance and ask an agent to re-sync the ticket), another option is to play around with the data you input for (in)SecureFlight - change the birthday is one place to start (my real birthday has never been submitted to SF). You can even try inputting a different gender - that might be enough to get you a 'pass' from their back-end check. The screener or ID checker never see the data you inputted, so there is no risk.

If you're truly on the NFL, you have two options - request a 'redress number' (good luck with that), or alter the name that you fly under ever so slightly so it still can pass the ID check and get OP mileage credit. Add or remove an initial, salutation, middle initial, etc. Sometimes a minor tweak like that is sufficient to get you past the list check.