Are you in the US? I would shoot out an e-mail (or make a call) to a trans legal organization. Look up The Transgender Law and Policy Institute or maybe the Transgender Legal Defense and Education Fund. In California, the Transgender Law Center can help.
If nothing else, you can drop a reference to such an organization as a not-so-subtle threat to this woman while you are busy changing your documents at the various agencies.
When are housing arrangements made? Do they have accommodation available in both dorms? I can see them saying, "Well, we're making housing arrangements NOW, and your documents say female NOW...by the time you get your docs changed, it will be too late!" But don't let them pull that.
Keep us posted. This is very interesting.
P.S. Sounds like that woman doesn't know anything about trans stuff. Did you tell her that FTMs can change their DL, Social Security, and BC without bottom surgery?
If you can change your BC and your license, that will certainly help. But I didn't know that any US states allow a BC change without surgery or a court order. Are you sure about this? I would love to know more.