I am no authority, but the prevailing opinion here on SDN is that you want to submit your primary app by the middle or end of June at the latest. You then want to complete your secondaries very shortly after receiving them. Prewriting your responses may help with this. Ideally, you want to be complete at most/all of your schools by the end of July or early August (or even sooner!).
I think
@sunflower18 is a great example of how having a strong application and submitting early can really help your chances (
http://mdapplicants.com/profile.php?id=26986). She submitted her primary app the first day AMCAS opened and was complete at most of her schools by early/mid-July. And she received 17 interview invites!! (As an aside, she has a wonderful MDApps page and thoughtful posts here on SDN. If you don't already follow her, I suggest you do! She offers great insight into the application process and I find her story inspiring!)
If you think your GPA really needs a boost, consider waiting out this cycle. Better to apply once with an awesome app!
Also worth considering, how much can one or two summer classes really impact your GPA? If your GPA is decent and the rest of your app is strong, those one or two extra classes probably won't help you out too much (IMO). But better to ask and AdCom, like
@gyngyn, about that, though. She'd be able to give you a better sense of how your situation may come across to your schools' admissions teams.
Best of luck!