In your case, the earlier the better, that will allow time to get your letters in.
June-July-August would be fine.
As far as interviews, they begin in Dec., but the bulk of mine were in JAN (basically the whole month of JAN about every 2-3 days!)
Most interview are finished by Feb. 1st, although a few programs interview later (very few), with the latest I heard being Hawaii (Feb 22nd), and not many interview in november.
I was freaking out, because I didnt hear from a lot of my programs until DECEMBER, inviting me for interviews!
Good luck to you, hope this helps a bit.
