Here is a paragraph from their web site at
http://www.abos.org
Potential applicants who have passed Part I must be continuously and actively in the practice of orthopaedic surgery in the United States, its territories, Canada or a U.S service installation for 22 months immediately prior to the examination. Of the 22 months, twelve consecutive months must be in one location. Time spent in fellowships cannot be counted. They must also hold a full and unrestricted license to practice medicine in the U.S. or Canada, or be in full-time practice in the U.S Federal Government.
Sounds like what you want to do may not work out. You can always do your missionary and come back and start private practice and then take the orals. The only catch is you must take and pass Part II within five years of passing Part I, otherwise you have to repeat Part I again. I would not want to repeat Part I again, especially several years after residency.