PHOTOS will help the gallery help you !
how thick is the floor ?
is it painted or carpeted ?
how much room is under the wood floor for a typical pedestal mount ?
in my world, I would cut out a 12" circle of the carpet,
covering, or whatever so you can get down to bare wood.
grind off all paint, epoxy, glue, etc down to bare solid wood.
cut a new piece of 3/4" exterior grade plywood to fit the circle.
Drill mounting holes for the pedestal base as well as holes through the deck to accept long bolts.
On the back side of the disk, rough it up with 40 grit sandpaper.
On the top side of the disk, bevel the edge to your liking and preserve it accordingly.
apply stainless fasteners
in the appropriate position. (once installed, impossible to adjust).
with the pedestal base fastened to the 12" new wood the way you want it,
glue the new wood disk to the deck. (once installed, impossible to adjust)
Personally, I would use "resorcinol" glue as it is 100% waterproof.
But, there are many good exterior glues, epoxies and adhesives on the market.
After the pedestal base is fastened tightly to the disk with 1-1/2" bolts,
coat the protruding ends with grease or candle wax and masking tape so the bolts can
be removed later. (or, they may become permanently embedded in the adhesive).
Once the disk is glued into place, THEN, you can use some stainless wood screws (not lags)
to help hold it in place as well as place some weight on the seat and let it sit overnight.
Read - Understand - and Follow the instructions on the label of any product you may use.
In my world, that is what I would do.