Ask USAA for help!
People say USAA is a great bank. Put that to the test. They should have a reasonable answer for this problem, yes? So call up their customer service and ask them what to do. Expect, and demand, they have a reasonable and workable answer that doesn't involve gold bars.
Then, don't fall into "Halo Error"... if they don't have a good answer, than acknowledge that. Hey, I'm an Apple mad-dog but I don't expect cutting edge features in their phones or top video cards in their PCs.
Borrow a bank.
You are absolutely allowed to have bank accounts at 2 banks. And it's not "cheating" LOL.
I think at one point, I had accounts at 4 different banks + 3 brokerages. Once I took unemployment... the benefits were paid to a bank's debit card which was highly inconvenient, so I just opened a bank account there because it let me access the money easier and with fewer fees.
Some banks have fees if you don't keep a minimum balance, but that's probably not a problem for someone who is liquid enough (and it sounds like you are). I was when I had those accounts.
In fact, a brokerage might not be a bad option for you, since most people can use a brokerage account, and USAA doesn't have a big practice here (they partner with Charles Schwab for most of it, and that might be the answer right there if Schwab has walk-up branches where you frequent). Find a brokerage that has walk-in branches most places you go. Deposits are generally FDIC insured unless they are invested in a risk investment such as a stock or mutual fund.