My plywood bed platform has to span a distance of 43 inches, from wheel well storage to wheel well storage.
I was also worried about the 'bouncy bouncy', fatiguing or just outright breaking the plywood.
I re-enforced the leading edge of the plywood with some cold rolled angle steel. I cut a rabbitt in the ~3/4 plywood and gorilla glued and screwed the steel to the plywood.
Now my sliding storage boxes fit under the bed rise to within 3/16 of an inch of the platform, but I can lie in bed and still slide out the boxes, so that shows how little the plywood flexes with the steel re-enforcement.
One of my wheel well storage boxes has a pullout that is also 43 inches long, six inches wide, and I use it as a bridge and pull the 48 inch wide bed away from the back doors to give more room. I also re-enforced this piece of plywood with 2 lengths of the steel angle iron. Unsupported by the storage boxes below, it holds up my 225 lbs when squatted in the middle while making up the bed.
The steel also protects the leading edges of the plywood from dings. Before I glued and screwed the steel to the plywood, I rounded the sharp corners and painted the exterior surface with flat black paint. Next to the dark walnut stained and polyurethaned plywood it is not too obvious.
If you are worried about the plywood breaking, I just wanted to convey my solution to the problem.