If you absolutely can NOT change your fourth year schedule, here is what I would do in order to get 2 SLORs into your file and get your ERAS submitted on time...
1. Pick an EM faculty you are familiar with at your home institution now and talk with them. Let them know you are going to do EM and ask them to mentor you,etc. Then, as fourth year gets closer, if you can't do a full rotation in EM before October, ask that same faculty member if you can come in and do enough shifts in the ED on your own time (i.e in July or August) that the person would be comfortable writing you a strong SLOR. That way you don't have to wait around for an official rotation to begin in the late fall/winter.
2. You will need 2 SLORs and it's best to get the other one from an away rotation (for audition purposes and to show that you can function out of your comfort zone). Set up your externship for as early in the year as possible (certainly no later than October or November if possible). You can go into ERAS and designate the letter writer and then get that letter in ASAP.
Bottom line is that interviews move early and fast in EM. I was surprised at how many of my interview offers came in before the dean's letter even came out on November 1. The rest of my offers (except for 2 programs I still haven't heard from) came in within the next two weeks. You really want to submit your ERAS as early as possible with or without the SLORs in place - but you don't want that SLOR missing for too long or you probably won't hear from many places (extremely important component of the application in EM)