This is what I have been told by my PD about the letters:
All schools require you to have your ERAS app, personal statement, and 3-4 letter's by their respective deadlines. By their deadline, the schools just want to make sure that you have the correct NUMBER of LORs. Now there are some schools that automatically download everything you have uploaded on your ERAS account the day after their deadline has passed, but most schools probably don't do this. Most schools probably wait until the day before your actual interview to download your LORs and other aspects of your app that tends to come later like the Dean's letter. So with that being said, while there is a deadline by which you need to have a certain # of LORs submitted, once you have reached that deadline you have the ability to swap out your letters to respective schools anytime you want. So with the most likely assumption that most programs don't download your letters until closer to your interview and the fact that you can swap your letters out after the schools deadline, then as long as you have the letter uploaded and swapped pretty close to your interview time you should be fine.
My cousin who just matched into ortho told me that he did a super late away rotation that didn't end until early november and got a letter from there a week later. He thought it was too late, but he uploaded the letter from that away rotation anyway, and was really surprised that at his December interviews the interviewer brought up that very same letter, talking about how good it was. Of course this is anecdotal, but I think it is an example of how the process works. ERAS is essentially a database which we, the students, can upload our application components, and the programs can download what we upload. When the different programs log onto ERAS and view our account, they see whatever files we have put there.
So yeah, I'm in boat as you, except I am doing an even later away rotation, but I am not too concerned. I will send in enough LORs to make the deadline, and swap them out later. Of course its ideal to have them all in for good by their deadlines, but that isn't going to work out for me.