NoCo, IMHO 3/4" is overkill. 5/8" would do it.
I like your idea to span under both coolers.
Another idea would be to laminate together two pieces of 1/4" plywood so you get even more plies (both strength and stiffness and minimize voids/weaknesses) in a thinner, lighter panel. I did this for the massive 36" x 42" stern cross hatch in my dory and it's bomber stout.
Your plywood floor is suspended on its "strong" axis.
Your plywood side decks are spanning their "weak" axis (long fibers of the wood face should span the supports, not across them). Have you stood on top of the wood while suspended and if so how much flex did it have?
And if it doesn't flex, you could go with a thinner ply running the correct direction to save weight.