The Polish medical school may indeed be a red flag. While PM&R PDs are all somewhat familiar with the major Carib schools, as a rule I dont think they are as knowledgeable about Eastern or Central European schools. The timing of the PM&R letter may also be an issue. My understanding is that it takes about 4 weeks between when your letter is submitted to ECFMG and when it gets downloaded into ERAS. So a PM&R letter not yet submitted will probably not be available by Sept 1.
From an IMG standpoint, it is generally better to get everything in as early as possible. Will this mid-September upload hurt you? Depends on your personal statement, other LORs, the rest of your application, and the individual program looking at your app. Some PM&R programs upon initially seeing an IMG from an unknown school without a rehab LOR or much other experience (so yes your age indirectly may be a factor) might pause.
I would suggest applying broadly i.e. not just to every single program in the NY area but also beyond, and also to a lot of prelim med programs. I know you would like to remain in the area, but you also need to cover your bases. Rank the prelim programs at the end of your primary ROL, just in case. Not to discourage you, but you should also prepare for the possibility of not matching into PM&R first at bat. If you dont, a strong performance the following year whether its clinically during internship or through a year of research or both will only serve to strengthen your future application if you decide to reapply.
Prepare for the worst, hope for the best. Good luck.