No clue as to what kind of rig you have. I see you want to stay about 6 weeks. You could stay two of those at Ft. Pickens. It is a very enjoyable place to stay. Buy a Federal America the Beautiful pass or Senior pass and you don't have to pay the gate fees.
https://www.recreation.gov/camping/fort-pickens-campground/r/campgroundDetails.do?contractCode=NRSO&...Edit: reread your post. Pickens does not have sewer, just water and power. They do have a dump station.
You mention Grayton Beach, so are you referring to your friends being on the EAST end of Santa Rosa Island? by chance?
If so, Henderson Beach State Park is quite close to Santa Rosa.
https://www.floridastateparks.org/park/Henderson-BeachCharles
'03 Ram 2500 CTD, 5.9HO six speed, PacBrake Exh Brake, std cab, long bed, Leer top and 2008 Bigfoot 25B21RB.. previously (both gone) 2008 Thor/Dutchman Freedom Spirit 180 & 2007 Winnebago View 23H Motorhome.