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The score you get from Amex BCE is Experian FICO8, I don't have BoA and Navy so I don't know what they provide if they do. You can get all 3 FICO8 for $1 7 day trial at Credit Check Total, make sure you cancel before the trial end date or you'll be charged $30 monthly fee.
NFCU’s Platinum has a low APR, you can even try to PC one of your current cards, I think that saves you another hard pull. If you can get in with USAA they also have a low rate Platinum card.
Why are you concerned with a low APR card? I get zero APR, as in the case of a BT card, but low APR suggests planning ahead of time to have to carry balances and pay interest.
TBH the days of good/low APRs are over. So the only way to combat that, is to either PIF or carry BT balances during 0% promotion period.
The typical APR seems to be between 16-18%, unless you go with a CU. Which it seems you have in those two NFCU cards^.
If you want lower rates, use you current cards wisely and ask for APR reductions. But it goes without saying, lower rates come with experience credit file and better scores. Also, since you're a student. You appear to already have a decent selection of cards, more isn't always better.
High HP/inq are going to count against you on a thin file, hence more denials. You might need to stay in the garden longer.
That said, Discover is good card to have and BofA has low rates from what I've seen. best of luck to you