The best advice I got was that if they're interested in interviewing you, they're interested in hiring you. The interview is merely a process for them to find a reason not to hire you, so don't give them one.
If you create the impression that your being transgendered is going to cause "problems" for them, progressive or not (Target generally is progressive), they're not going to hire you. If you're full time and your legal documents support that, then by all means interview that way. Say something, long after the interview, long after you're hired, about being transgendered if you need to. Though keep in mind, if you wait until they're about to fire you, its too late.
If your legal documents don't support your female gender, I'd be willing to be they'll let you know "we'll be in touch" and that will be the last you hear from them. Does it suck? Yes. Which is going to delay your transition more? Being unemployed or having to work a probationary period as a male? I'd wait until your probation is up, as we've pointed out before you could find yourself on the receiving end of "its just not working out" otherwise.