You can use a handheld power planner to make scarf joints on the plywood if you're careful. And by using gorilla (or other expanding) glue it'll be as strong as the original material. You need an 8:1 profile for the scarf joint.
If you know someone at a cabinet or boat making business they may cut the joint for you.
Marine plywood will be stronger because of the number of plys, but exterior grade would work if you don't want the expense of marine plywood.
Having said all that, using two sandwiched pieces of thinner plywood would work if you glue them together completely. I'd also recommend double staggering the joints by notching half the sheet back a foot or so.
By flipping the pieces around and over and gluing them 100% you make a very strong floor piece.