I'm pretty sure the 2-week secondary rule has been repeatedly disproved in every cycle. I have no idea who started this, but this "rule" seems to be an outright myth.
It's good to complete secondaries early, but high-quality secondaries sent after 3-5 weeks are far far superior to crappy secondaries that are hastily submitted in the 2-week turnaround.
IDK man if I was a school, and someone took 5 weeks to send in their secondary, I would take that as a sign that they dont exactly have me as their top priority. Why should that school then have that person as a top priority?