Florida
Sorry man, What your looking for does not really exsist in the Florida Keys.
The keys are just feet above sea level and are a soft, pasty softened limestone. Its like white clay.
Any beach is man made and the sand is impotrted and usually found at higher end touristy resorts. Its expensive to make a beach due to erosion.
Secluded - My FAVORITE - we think alike!
OK...........I have taken a few ladys on the experience you are wanting. Every one LOVED IT !!!! Its paradise. Naked providers on pristine white sand beach's with beautiful clear tourquise waters - Oh my .
Google Exumas Bahamas. I go to Staniel Cay - google it.
Single runway. Google Watermakers air. They charter a flight there once a day and rent 3 beautiful villas right there. As long as you don't overweigh their plane you can bring whatever you want - its a chartered flight. From Ft Lauderdale directly in - about 1 and a half hours - really quick !
Can rent sea doos or a boat. Bring your GPS for corrdinates so you don't get lost.
Many millionares visit with their yachts and party at the Staniel Cay Yacth club.
You Tube has quite a few videos - enter Exumas in the search feature.
These are probably the most BEAUTIFUL SECLDED beachs in the world - Next to Fiji in beauty, and I have been on a MILLION beach's - I'm a PROFESSIONAL !
I rent jetskiis for her and I, load the front with ice and adult beverages and just fly around all the islands. Find one all to yourself and relax and fuck - right there , no one is around !!! They are secluded !!!
Go to Sampson Cay and swim with the pigs ! Yep , swimming pigs in the tourquise waters of the Bahama's. 20 people live on Normans cay. Single runway and 1 bar - McDuffs. Tell Kat I said hello 
She rents out 4 rooms above the bar. Watermakers air WILL fly you to Normans Cay or any one that has a runway, but Staniel Cay is their "hub" so to speak.
Bring your snorkling gear and snorkle where the James Bond Thunderball alley was filmed. Hell, you can snorkel anywhere really.
Again just research the places I have listed on Google and You Tube.
Have fun and fucking on a beach is great !!! But sand can be quite a pain in the genitals if you know what I'm sayin
-- Modified on 10/1/2012 4:21:06 PM
Found that little gem about 7 years ago. I knew of Carlos Leiders story, and his dilapitaded old mansion is still standing , barely I read a book about his escapades written by his piolt - crazy shit and a great read ! If you can find it, I recommend reading it while relaxing on the beach with a beer from McDuffs
Mc Duffs is all that is really there. Kat owns it and rents out 4 rooms above the bar - about $120 a night I think.
Runway could use some work but that would take away from the ambience
JUST love the Exumas !!!
Go visit again - no worries.
Just ask watermakers air if they can fly you directly in. You could catch a boat ride from someone off of Staniel Cay if you asked around.