One of the things you'll have to watch out for when you apply for a job, regardless of which state it is in, is your SSA defined gender.
If you apply with your current SS number and list yourself on the job application as female, but SSA lists you as male, it will bounce back. Also, if your job offers health insurance, the gender mismatch could come back.
If you are applying to the job in stealth, then you could put your job in jeopardy. If they know you are in transition and that your records will be appropriately amended as time goes along, then they may accept your condition.
Additionally, the listed rules can sometimes be "bent". I applied in person to record my legal name change to the SSA office and as the person was going through the process, he simply looked at me and asked "Do you want me to change the gender too?" Of course I said yes. I tried not to jump up and yell YIPPEE until I got out of the office though.
I can't say that this would happen for you, but it certainly is worth a shot. The worst that could happen is that they say no.
-Sandy