Here are a few other things to consider. Will you be putting down your current job on your job history? If so, a prospective employer might want to get in touch with your old boss. I don't think it's very likely, but it's possible.
Have you changed your sex marker on your driver's license? I'm assuming that your sex with the SSA will stay the same, but I understand that the SSA isn't sending out "mismatch" letters anymore when the sex marker doesn't match what they have on file. This should give you greater flexibility.
If you haven't changed your name yet and plan to, will you change your name at the old job? Think of the advantages and disadvantages of doing so.
As you pointed out, the economy isn't so great. If you want another job, you're better off looking for work while you are still employed. If you're not getting any nibbles, you can always go to Plan B and stick with the old job.
Is it more important to you to be working or to maintain your privacy?
Can you get a job on campus?