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Thanks Red, very interesting. I appreciate your thoughts and wisdom on this. Sincerely Thank You.Typical heated slab is for snow melt driveway would be dug out to allow for material thickness. Then a layer of stone for drainage, vapor barrier plastic sheeting, then foam board insulation, then 4" slab over foam to finish height. In your case the foam board would insulate the ground, significantly reducing the frost depth of the area under the insulated area. You can extend the insulation past the slab and burry with dirt out say 36" beyond the outer posts. When finished it a concrete slab with lawn coming up to the edge of the concrete.
Here is an illustration of the rough principal applied to your situation. Disregard everything other than the slab construction in this illustration:
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