Like you just ran into, most companies require a current Class 1 to even apply. If you're mil overseas, ask the flight doc's office if there are any AME's on staff there. Otherwise you might have to get it the next time you are in the US. There are only two times it would matter if you have a curent one; when you apply and when you interview. If there is some time between the two, and it expires, get it renewed before you interview.