Hi,
I did an Army residency at WRAMC and I’m Navy. The Navy made an exception for me to do the program and the Army and ACGME both made a spot for me. So it does happen,
In terms of residency, you should always try, because all they can say is “no.”
And it’s like marriage, you should marry the one you love, not just the one who’ll have you.
Good luck to you,