Many thanks, Dave --
I recall looking at your and Paul's photos and having a pretty good feeling about tackling the floorboards on my boat. Now you can understand my chagrin when I discovered what a nightmare I was up against once I removed the side panel.
I think Mike Watson's suggestion is the best approach: basically separating the 'glass from the plywood with a small prybar, removing the floorboard, duplicating the floorboard and recovering it; and reinstalling it, this time simply with external screws. He wisely suggests "wear gloves." Sheesh, this is much bigger than I bargained for.
On your question about whether my oddball flooring may have been done by a previous owner, I don't believe so. It looks like "factory work" to me. The fiberglass on the inside of the hull matches in color and mesh with that of the fiberglass mat that curves out from the hullside and is epoxied to the floorboard. Even the screw holes on the inboard edge of the sheathing is fastened with numerous brass, countersunk screws that are professionally covered with putty. Also, the mechanic at my marina says he has encountered very similar construction on other CC boats, and he simply cut the floorboard out with a skill saw set at a depth only a hair deeper than the board width (3/4" in this case).
Thanks, again, for posting your photos. They're great, and I wish my boat was designed that way.
A couple of questions--for now

-- what paint did you use for the wood frames and the back of the floor sheathing? Also, I have a quart of Nautolex adhesive. Will it adhere to an unpainted side of 3/4" marine plywood?
Wish me luck!
Best,
Cliff