Perhaps the best way to join two sheets of plywood is to scarf the joints. Making up a scarfed joint isn't especially easy, though; and clamping it can be rather tricky. Properly done, it's basically as strong as unjoined plywood.
Your laminating approach would probably work okay, though I'd use normal wood glue (such as Titebond III, which is waterproof) rather than contact cement and find a way to clamp things solidly. If you have a flat, sturdy floor to work on, you could probably clamp it adequately by piling several bags of sand on top. That might not work so well for a scarf joint, as the joint would tend to slide apart downhill somewhat.
Realistically, though, replicating what the factory did should be good enough, since it was strong enough for many years on many vehicles, including yours until the water damaged things. There's unlikely to be a lot of weight on the outermost foot of the bunk board. (You also might be able to find 6x8 sheets of plywood with some searching around and avoid having to make any joints.)
