So long as you pass USMLEs, have US citizenship, and are articulate in English, I think you got a decent shot.
You got to things that are out of the norm that will not make most programs want to go out of their way to get you, but will make several programs do so...
Bilingual in English and Spanish (maybe more)?
And you got an anesthesiology background.
The reason for the first is obvious: There are several areas of the country where the only language spoken by several people is Spanish and several of the doctors in those communities don't speak it. You could be a boon to a hospital in such an area such as Florida, Texas, California, New Mexico, New York City, etc.
The anesthesiology thing: it's rare, but when it happens you want anesthesiology involved in a case where some patients will not be sedated despite mega-doses of medications. There are a few existing psychiatrists with an anesthesiology background, and when patients get agitated, these guys can always take such a patient down.
On occasion, you get a patient where they are dangerously agitated and not calmed down or sedated no matter what you give them. I've seen this happen a few times--e.g. Thorazine 400 IM, Haldol 30 IM, Ativan 4 IM, and the guy is still up at at 'em, swinging punches.
I'd definitely want at least one person in the dept with such a background to be called upon when such a difficult case occurs, so that person could look into what could be done outside the usual psychiatric choice of meds. When we psychiatrists call upon anesthesiology in these tough cases, they often times are too timid to assist us because our training is so diverse and we usually don't interact with each other.