I think getting into the reserves is your best shot at promotion bar none. As a Navy FTS working at a NOSC, (a full time reservist working at a reserve center), there are boatloads (pun intended) of passed over 0-3s who picked up 0-4 with their reserve unit. You won't get flight time, but you get promoted, you get paid and you get benefits, plus there are tons of airline guys who could give you that all important internal rec......
Not to pile on with the other guys, but I think the Navy flying gig is done. As a guy who spent two tours in orange and white I can tell you that those boards are VERY competitive AND they will look at your quals thoroughly...and unfortunately your record will not make it though. I apologize but I want you to succeed and not waste time chasing things that won't pan out.
Please feel free to PM me if you have any questions about going SELRES or the training command.