Good question. There are a few separate things to mention here. Firstly, of course with rolling admissions, getting in earlier will be helpful as there will be less competition and more seats available. We suggest getting in the primary application early July at the latest and the secondary applications late July, or early August at the latest. However, if you have stellar stats, you may be able to finish secondaries in Mid-Late August.
The MCAT: Because you already think you are a less competitive applicant, it will be important at ace this test. If you haven't already, you should be taking full length AMMC practice tests. You can use half of your time studying for your weak areas and the other half as a mixed review. It is not ideal to take this test again, so ensure that you give yourself plenty of time to prepare and study. We suggest that students don't take this exam until they are scoring in the 90th percentile of the practice tests.
One of the best resources for you will be the Medical School Admission Requirements (MSAR) website. To unlock most of the features you will need to pay for a subscription. You can look up most of this information on your own, but it will take you more time. You should look up the stats of the schools you want to apply to, and in particular, the average accepted MCAT and GPA scores for the previous year's matriculating students. Then you will have a good idea where you stand, and which schools you have a decent chance of getting in. If you have not taken the MCAT before, you can use your most recent practice test scores. You can also see which schools require shadowing and other experiences.
Best of luck!