Are you going to submit your primary after you take your MCAT or after you get your scores?
I submitted in early August after I got my scores, took 6 weeks to get approved, and another month and a half for my committee letter to go out. If my committee letter had gone out sooner, I may have gotten more interviews (I really wanted a shot at VCOM), but since WVSOM (and Lecom) invite for interviews without secondaries or letters, they were the first schools I heard back from. I got my interview invite for WVSOM in October, about 2 weeks after my primary was verified, and my interview invite for LECOM on Halloween. Interviewed at WVSOM in early November, accepted 11/27, interviewed at LECOM three days later (they waitlisted me.) LMU-DCOM called me the week after my LECOM interview for an interview invite, but I had already accepted my WVSOM seat at that point. ACOM emailed me just after Christmas for an interview in January, because I apparently forgot to email them and withdraw my application.
Anyway, try to submit as early as possible, especially because you're an underdog, and especially because very soon it will take 4 to 6 weeks for your primary application to be processed. You can select one school to apply to, just to get verified, and submit without taking your MCAT if you indicate the date of your MCAT, and then go back and add in your scores when you get them. You can also add more schools at that point. That way, since you'll already be verified, your primary application will be sent right away to the schools you choose.
Your chances of getting in are much better early on, before the schools swell with applications, because the people with the "average" numbers will be submitting in September and October and by December the "nervous" MD applicants will be submitted.
