You're correct that in DC, handicap spots are noted with the red-capped parking meters. Admit with explanation, plead that you're an out-of-towner and didn't see any other sign or marking indicating it was a handicap spot, and maybe the hearing examiner will have mercy on you and reduce the fine. If you straight-up contest it, you'll lose and will definitely be paying the $250. With AwE, at least there's a chance.