I agree with dbiddy. Getting a LOR from an October rotation can mean really having it in your hands and in ERAS sometime in November, realistically. This assumes you ask near the end of your rotation and letters just don't spit themselves out automatically. You will likely have interviews in December, possibly 1-2 at the end of November so you need need need to have a month of anesthesia done by that time, which it sounds like you have covered. Now as to how to get a letter earlier...you've got July and August right? If it really is too big a pain to rearrange your schedule to allow a September elective then shoot for some serious shadowing outside of your July and/or August rotations. This will help you in numerous ways, number one being you get more exposure to the field and if you had to change your mind it won't be too late for ERAS, and number two being the all important letter. Anesthesiology is a 24 hour field, so you can always find someone in house. Explore a bit, maybe find a community hospital. Those guys don't get students as often and are usually very receptive to having someone around. Now this doesn't mean spending every night on call with someone, but if you're on psych or something like that you have plenty of free time so use it.
FYI, I did my elective in September last year, applied to ERAS with no anesthesia letter. Got some interviews before the letter even got there, letter came in early October and everything went fine for me. Good luck!
