1. Has anybody used the Star-Spangled Banner on their Part 15 station for sign-on/sign-off?
2. If so, were there licensing fees charged to you?
The U.S Army Band begins and ends each (rather sparse these days.....!) broadcast on my Part 15 (3-A Oldies 91.9).....
The song itself is Public Domain. You may use it freely. If you are BROADCASTING OVER THE AIR ONLY you will have to pay NO license fee, as over the air RADIO does not pay the ARTISTS only the WRITERS of songs. So, over the air, it makes no difference.
STREAMING however, DOES pay the artists as well (That's what your SoundExchange license does). So if you are streaming, you would have to be licensed for SE unless you're using a Public Domain recording, or performing it yourself. But, if you're streaming music already you should have your proper licensing in place already, which would also cover the anthem.
TIB
It is my understanding that products of the U.S.Government are public domain, which would include this recording by the Army Band.