Applying early is not only primaries. Don't think you're safe if you submit the primary with 30 schools on the first week of June... only to get bogged down with the sheer # of secondaries later (my mistake).
If you do apply to a bunch of schools, either churn out secondaries relatively quickly, or if you're a slow writer then prioritize them.
One more thing, and I don't know if this really exists, but I've observed a couple bottlenecks along the cycle. There's a bottleneck in the primary submission where if you're submitting the primary on first couple days, the turnaround time is practically the next day. This turnaround time turns to weeks after a few days.
As for MY secondaries, I received practically all my early invites (september) from secondaries I submitted before late July. I presume this is the period where the majority of the early applicants have turned in their secondaries, and turning it much later than this leaves you in the middle of a much larger applicant stack, so to speak...