PrawsBlawg has some interesting (albeit limited) submission data for the fall law review cycle. As we see in other contexts where there is perceived to be a first-mover advantage (e.g., clerkship hiring), submissions and selections have moved forward in time. Based on a sample of one law review (BYU), it looks like the bulk of submissions are occurring in mid to late August. Given the common practice of simultaneous multiple submissions, there is no reason to believe that other law reviews are seeing a substantially different pattern. You should keep this in mind if you are working on an article next summer.