This would be a nearly intractable problem in a normal year - South Florida on short notice over a holiday weekend. This year? I hate to say "forget about it", but it's hard to think otherwise. You're looking for a set of things - President's day availability, South Florida, high end, points redemption availability, in-chain for MR, quiet beach. You might be able to get some, but probably not all.
My first thought was maybe a middle Key (e.g. Largo, Islamorada, etc.). But the few properties there (CYs/FFs) are selling for $600+/night and no points availability. So not that.
Looking at points availability across the board, there are a few things in the Miami metro area, mostly inland a bit, and not the nicest places. Same w/ SW FL e.g. RSW area.
If you are open to changing plans, the only other thing that comes to mind would be Puerto Rico. Looks like you can get nonstop Jetblue flights on your days, and do La Concha for 280k points for the dates you mentioned. I know PR has been popular, but based on the market test (point availability) it looks less so than S. Florida. And if you are willing to rent a car there are plenty of beaches you can drive to. Heck, you could drive out west and stay at the Courtyard Aguadilla for 88k for the whole trip and hang out with the surfers...