getting passports is the way to go, but i would think that r&r locations should be available thru the military....surely, going to germany should not be a problem and then going around europe....
the people i see on r&r at us airports are all in bdu's and are traveling w/orders [i think]...i always try to give them a high 5 and/or a drink coupon in the lounge... they may not have mufti, but could get some in europe...
have you contacted the state dept? and do you know what they would like to do?
places that come to mind are puerto rico, usvi, guam, pago pago...
good luck and a high 5 to them...