I would get new plywood and screw it down directly to the existing floor - It might add a little weight - but will be much stronger with double-ply floor.
Usually, the floors on those are not good quality plywood anyway, but even that will hold strength when screwed together.
Screw it down approximately six inches O/C around the edges and twelve inches O/C in the middle and you should be good to go ... and for that little added weight, you'll have a strong floor. Especially for a golf cart.
I'd use exterior grade 3/4" plywood and use a good quality oil and grease resistant garage flooring paint.