Hi, Andrew! You're certainly not alone. I hate my old name now. On occasion somebody I know still slips up and uses it, and it makes me mad. On occasion I still get a letter from some relative I'm not out to, and I don't like that, either. I suppose part of it is that I do look quite feminine, and so it makes me mad when somebody uses a male name with me.
As for your problem, if you deal with your customers over the phone or by e-mail, then they don't see you. So can you not just start using "Andrew"? I suppose that could be a problem if your voice is still fairly high. If it is, there's another solution I've thought of: perhaps for a short time, until you're out full-time, you could use a "unisex" name. (What do you call a name that can be used by either sex? "Mel", e.g.)
Obviously, you'd prefer to use your real name, but if HR would go along with a temporary name, then at least you wouldn't have to be using your old one. I can well understand that you'd hate it. I don't really know if this would be a good solution. Just something I thought of.