This is a question to ask the actual letter writer. How will anyone here (assuming that the clerkship director isn't here on SDN) know when unknown program will upload your SLOE? Talk with whomever is writing your SLOE (usually the clerkship director or PD) about your time frame and if they have an idea about what the turn around for SLOEs are. It varies a lot by institution. As a student, I got my letter back from my current program super fast in the midst of audition season. Other programs needed multiple reminders (one admitted they just forgot).
It is highly unlikely that the SLOE will be available by the time ERAS opens. I wouldn't worry about it too much as most programs don't start reviewing apps until early October at the soonest. This of course varies but look at previous years' invite threads to get a sense of timing. I wouldn't worry about it too much unless you could schedule an audition for sooner. Since most students want to get their auditions done well in advance, I'm going to assume that these dates are the best you can do under the circumstances. Try and relax and make the best of the situation.