....OK, maybe I'm just not romantic here, but....if you aren't going to propose to her until the game....why would she wear Nats gear under Brewers gear....and wouldn't you rather hear her answer before you start taking off both of your shirts....that's a lot to squeeze into what might be 30 seconds....especially if you havent rehearsed it
Maybe I'm being delusional in thinking this could happen, but I'd try MASN. Tell them you're a long time fan from Expos days and want to propose to your gf with the added caveat of being a Nats fan.
The jumbotron thing seems so cliche nowadays, and your situation as an 'away' fan at an away game is unique. I could see trying one of two things - less ideally, see if MASN would work with you and televise it - Jumbotron equals 20,000. TV is both far reaching and captured for all time. Like have the sideline reporter come down, seem to randomly interview you, then you pop the question.
The best of the best is if MASN could facilitate the team's involvement. I could see like trying to get a seat behind their dugout, have a player roll-hand you or her a ball 'autographed' with "Will you marry me?"
Or sitting in the same place, if you could have a few players turn around, wave/call her over and then say they have a question to ask her. Then have five or six players each ask her to marry them, until finally you're behind/beside her on one knee and tap her to divert her attention to you, and pop the question.
I really think with the out of town aspect, you've got a damn better chance at something crazy than just another bloke going to a local game to propose in front of a bunch of people. Definitely don't have anything to lose e-mailing MASN or trying to contact a big wig, whether Bob, FP or someone beyond a generic MASN Contact Us e-mail.