why wait for the independent study time? That seems to me like saying "ill start studying for the mcat during spring break right before the exam."
There are two winter breaks and two spring breaks during years 1 and 2. Most people also get a nice summer break between M1 and M2. Additionally, I think even in the toughest of schools, you are not working ALL the time. There are weeks here and there without exams where you have some free time to study a little here and there. Dont put it off til the last minute. After all, it is YOUR responsibility to make time to study for the boards. Take advantage of your free time.