I have been working on applying to ortho schools for the last 2 years, from bunch of applications number, I only got 1 interview. Although I really was great at my foreign dental school, president awards, best students, research won prices nationally, scholarships, international orthodontics program (1 year), still very very hard to compete with the US graduates especially your vocabulary score of your GRE is quite low in compare to the native speakers.
They will look on GRE, National boards (usually above 90), and heavy research experiences during dental schools, and of course, recommendation letter or connections to the ortho schools you applied for.
I know that at least 1 from the residents in some school will accept 2 year IDP graduates, I am talking about top ten orthodontics schools.
A lot of school said they would consider foreign trained, but in reality, they just throw that applications down to the garbage can.
Not all the schools do that, some schools accept numbers of foreign trained, and for some weird reasons, once you are a citizen, you literally can't compete with foreign trained, but US graduates instead, makes is even harder to compete.
Being a citizen has drawback from being just permanent resident in term of your status. Yes, you could apply for IDP program who only accepts PR and CItizens, but in the specialty program, once you are a citizen, you compete with other citizens (US graduates). I know one school has this policy. Again, not every schools are the same, you have to study each of the characteristic of the school.
Some schools have the feedback from residents during interview, and some schools just mainly choosing based on the faculties feedback.
Saint Louis accept many foreign trained dentists, UIC accepts 3 foreign trained dentists, BU and Nova.
I think it is safe to say by going to the IDP program first, you have way more options in pursuing your specialty world. Orthodontics is one of the most competitive program in the US. If you want to be more less competitive, try perio and restorative dentistry.
At U of Michigan, they accept a lot of foreign trained into restorative dentistry.
Just a thought.