I didn't end up losing my job 3 years ago, but it looked for me at least as possible as it does for you right now. I don't think preparing to work in a new job is a matter of surgery, but rather of clarity. At the time I was worried about my job, I had been presenting full time female for 3-4 years, but I was still using my old name. My counselor pointed out that if he were interviewing me, my presentation would be coherent and non-problematic, but my name would confuse him. Most potential employers won't care if you are transgender, but if they are confused about what you want and expect, they might feel uncomfortable, decreasing your chances for hire. It is not difficult to tell that I am transgender, and they can deal with that, but as long as I kept the male name, I was throwing off mixed signals.
Hiring discrimination still occurs (and should be reported if there is evidence to support the claim), but I submit that getting hired by an anti-trans company then coming out later will be no picnic either.