As an African-American performer, I have to say that I completely relate to the difficulties of Asian-Americans being cast in musical theatre. Although it is SLIGHTLY better, and I mean, SLIGHTLY better for us casting wise when it comes to diversity, it still is difficult, so please don't be disillusioned when you think it is easier for other minorities. Just like you, we fall into our own specific categories in casting, and have the same concerns as you do.
Although you might feel that you may only get cast in shows like "South Pacific", "Flower Drum Song", and "Miss Saigon", Blacks and Latinos have their own shows that they constantly have to rely on - that being "Ragtime", "Ain't Misbehavin'", and other shows like that, which either require specific casting requirements, or need a specific singing-voice (a BIG BLACK VOICE) type for the roles. And for Latinos, I am sure "West Side Story" is also a no-brainer...
I DO have to admit that diversity is getting better in more of the streamlined/traditional shows. I have been cast in a lot of roles that were not traditionally of any specific race, and I have seen quite a few Asian-Americans in large roles too....I can recall seeing an Asian-American "Domina" in "Forum", and an Asian-American "Frumah-Sarah" in Fiddler. In all honesty, I don't think your situation is all that bleak....you just need to find theatres that have directors and production staff that are willing to be more open artistically with casting.
In this day and time, I still do come across "bigots" who can't think outside of the box when casting, but then I move on, and keep auditioning, and eventually come across people who try different ways to cast roles, and it works. I do find that the more professional a production is, people are willing to take more consideration into color blind casting. And even then, it doesn't happen all the time. Color-blind casting can TOTALLY work, and I am a witness to it. So don't be so disheartened. You will be fine. Your talent, and determination will help you find the roles that you deserve, and the people who are willing to give you a chance.
Would you be seen as an "Audrey" in Little Shop? I can't completely say yes.....maybe someone with the vision would cast you that way. I personally always see Audrey as blonde, but then I cannot get the "Ellen Greene" visual out of my head for that role. There is absolutely no reason why it couldn't theoretically work.... Sometimes, it comes down to something like that when casting too, and it is nothing personal.....
But like I said, your talent can sometimes make people want to take a chance on you, and help them think outside of the box.
Just my 2 cents.
Cheers,
The Balladeer
"Someone tell the story...Someone sing the song...."