I believe strongly in property rights as well, but I also understand that real property law is complicated and property rights vested in owners are not always absolute and unqualified. I'm genuinely interested in the views of BFO owners. Which leads me to ask 2 questions of BFO's. For your personal parcel, has the public never used your dry sand area for recreational purposes during the time you owned it (and you can exclude the short period of CU by ordinance). In other words, do you believe your dry sand has always been treated as private? Second, if CU was defeated and I showed up by myself with a fishing rod and a chair at 6:00 a.m. and sat 10 feet out of the wet sand on your property, would your intention be to ask me to leave? I expect I'll get a cavalcade of responses that you want the right to tell me to leave regardless of whether you exercise it, but I'm asking what your approach would be as a pure matter of personal interaction. Is that what you would do?
Well let's start with your first statement. Property rights are absolute (read Tiffany) unless limited by law. Unfortunately, many here want to define by fiat what property rights are or are not on beach property and run to the "rights are not absolute" argument. So I reject your premise and you might want to spend a few days reading Tiffany on fee simple. No doubt real property and land use law is complex - but that complexity doesn't default to limitation, but the opposite.
As to your next two question - no the "public at large" has never used my parcel or most private parcels in Walton county. If you mean have random non-owners occasionally used the parcel --- with or without my knowledge --- well that's a given. But you didn't ask that. You asked if the "public" used it and that means something entirely different - the public means everyone and anyone, in any quantity, continuously and notoriously (not covertly) and the answer is "no".
Second question. First I would not have any knowledge you were there as I would not be awake at 0600, and ten feet off wouldn't really catch my eye if you were there when I was. If you MADE yourself noticeable by staying there all day and returning day after day, and/or setting up camp, or loud noises or bothering people --- yes, I would inform you this is private property and you need to do this somewhere else. The key here is, are you making yourself a nuisance or presenting your presence in such a way that suggests you are "occupying" my property obnoxiously. And no, you don't have "Customary Use" --- you have CONSENT.
This is a core legal problem with custom vs. public trust. You and the residents of Walton county may have some degree of claim of custom on a parcel - what does not transfer is that into a public easement. This is why there are 7 criteria of custom - one of them being "certain persons".