OK, guys, here's how I'd do it....
First, I don't trust toggle bolts and the deck skin is too thin to use toggles for a chair mount. You need a substantial backing plate and this will give you that without having to tear up the deck.
Cut a hole 2" smaller in diameter than the pedestal base. Dig out the foam to a depth of 2", undercutting the foam 2" under the hole opening. Cut a piece of 3/8" aluminum plate into a disc 3" larger than the pedestal base, then cut the disc into 4 equal sections.
Using thickened epoxy, to the consistency of catsup, fill 1/3 of the void depth and allow it to self level and cure. Once the epoxy is hard, but still tacky, place the aluminum sections in, one at a time and position into center. Now fill the remaining void to 1/2 it's depth and let it harden, but still tacky. (thicken the epoxy with milled fiberglass for the first pour and chopped strand for the second and third pour.)
Finally, slightly overfill the remaining void with epoxy, let it completely harden for 72 hrs and grind/sand the surface back to flush with the deck.
Place your pedestal, centered over the epoxy filled hole and mark the bolt holes of the base. Carefully pre-drill through to the foam and tap the holes to the appropriate size bolts. When you bolt the pedestal down, put a dab of 5200 in each bolt hole and a ring of 5200 for the base to sit into. Once the base is tightened down, wipe away any excess caulk and clean up the residue with acetone.
