Actually, I waited til 4 days before the application deadline to do my LSAT writing. They sent my CAS report 4 days after the deadline when the score still wasnt in. It was approved the next day (taking a total of 9 days after taking the exam). I looked it up because I was confused as to why my CAS report would be sent before LSAT writing was in and here is what I found: https://blog.blueprintprep.com/lsat/the-recent-changes-to-the-lsat-writing-section-and-law-school-applications-explained/

There's also a thread on reddit somewhere about this. Basically, schools were just as not happy about reports being delayed so they complained to LSAC and they changed the policy. You should be fine.