If your voice is getting you clocked, you need to work on it immediately. And it will take time to rectify. Read up on it, and get the software necessary to properly evaluate where your voice really is. (You don't want your voice dipping below 160 Htz, and your average baseline should be around 220.) There's also the matter of timbre.
Likewise, take care of your beard shadow -- electrolysis is your best bet.
While you're certainly passable in Western culture, I do wonder if other Asians would clock you based on your jaw/chin/forehead. And even if you're getting by, there's something profound about facial surgery. Seeing a different face in the mirror, one without the tells you've grown so accustomed to. I was doing just fine in the real world before I had my facial work done, but afterwards... I stopped clocking myself in the mirror. And that, as it turned out, provided immense relief from my dysphoria.
All that said, if your voice is spot on, it can overcome an ambiguous reading.
Finally, when looking for work in the midst of transition, a lot depends on how you're actually presenting yourself. A lot of employers aren't going to want to deal with the headache and heartache of someone who's actively in transition or visibly/audibly transgendered. If you're presenting as female, but your paperwork says otherwise, that's going to throw up all kinds of red flags.
On the other hand, there are some jobs out there that if you can get the work done, they won't care. Things like phone work, for example, which actually could be the perfect opportunity to practice your voice.