I am not sure if I can answer your question directly, but let me offer my experience which may help. I am a newly graduated resident from a school I would consider somewhat prestigious in terms of psychiatry training. My scores were very similar to yours when I applied and as a result I applied to around 30 schools netting only 9 interviews. I matched to my first rank program.
Now the field of psychiatry has changed since I applied, and from what I have seen and heard from my colleagues it has gotten a lot more competitive. If I were to apply again, with the knowledge I have from seeing 4 cycles of residency interviews, I would approach the application process in two separate ways. 1) Get interviews 2) Be genuine.
The first is that I would apply to as many psychiatry programs as I could (dependent on your financial situation). What you want are interviews, the more the better. At my program once you were offered in interview, it was a signal from the department that yes "on paper" you would be a good fit for our program. They did not offer many interviews in comparison to the applications they received. I applied to 30 programs or so and received 9 interviews. Although there were some "strong applicants of interest" prior to the interview, our program genuinely compared everyone at the end of the interview process fairly. Many times those strong applicants were not so strong in person, and other times there were some strong surprises from other applicants.
The interview itself was a test in which residents and faculty would get a feel for who you were. They were looking for residents who would compliment their program. I cannot tell you how many times residents during the final review process were put to the side because someone (faculty or other residents) determined that their might be a red flag. A red flag will be highly dependent on where you are applying. In other words 2-3 drinks on the west coast may not seem like a red flag, but ordering 2-3 drinks in the midwest may seem like one (true story!). The best bet, is to be genuine. You will match at a program in the end that will truly value who you are as a person. It is pretty easy as psychiatrists (even as residents) to see if a person is faking who they are. And plus you don't want to act fake and match at a program that won't mesh well with who you are.
In summary, if it were me I would apply to all the psych programs I could. I myself don't like FM and would never apply for it even if it was my last choice. I would then go to all the interviews I could and try to just be normal. In the end, if I didn't match (and I know plenty who haven't) I would do an extra year in school (work with your medical school) and reapply the following year. Try to get to know people at your home institution's psych department. Then reapply. I know some of my colleagues that matched into FM because they were not competitive in other specialties because admin told them to. And you know what? They hate it, it wasn't their passion. They are all trying to figure a way back to what they wanted to do. If Psych is what you want to do, then do it. Don't let one decision dictate your life.
Hope this helps! BTW of course this is just my experience, and others out there may have different ones. Good luck!
