BA probably won't be willing to mess with the reservation, as they don't "have" it. I've had luck getting CX to do a res for me on a BA ticket. They needed the ticket number for a PNR they created for that segment, and I got the idea they were more or less doing me a favor. A less enlightened carrier might have refused.

If AA's only rtw desk is at DFW I suggest you call when they're sure to be closed. If an ordinary agent is willing to help you, and you explain that you have this open-dated (first class?) ticket and now want to pick a date, they might think it was an inoccuous enough request to do it for you. I've had that happen with an ordinary BA agent on a BA ticket that did happen to be inoccuous (but he screwed it up.)

No doubt it will work out no matter who you talk to, but unless you're totally immune from worrying about anything, it's a crummy spot to put yourself into. Not that there's ever been a recorded instance of enforcement, but you will have violated the ticket conditions and the alliance will technically have your most prized possessions firmly in their grip, well within their right to squeeze as they see fit.