It may be too late for you, but IMHO if your program was like mine, take your exam during for 4th year. Reason being is that PGY IV at most places as far as I know is easy. You'll most likely have the time to study for it.
Taking the exam during your first year as an attending has disadvantages. You might not be in an academic setting to ask professors about questions you may have. It's also frustrating to make yourself studying after a full day of working hard.
If you work at a new job, it's going to be like doing a completely new rotation. You're not going to know how to do a lot of easy things that became 2nd nature in residency. E.g. putting orders into the specific institution's system, etc.
IMHO forget about studying for the boards for the first few weeks you do your new job, unless you work at a place where you already are familiar with the setting.
Another issue that may limit the jobs you seek are several places want a psychiatrist with at least 2 years of post residency experience before they are hired.