Laminate it like a butcher block and install it in one piece?
Installing a single piece in a '53 bed would be a trick. You'd have to remove the front panel and slide the single piece in below the angle strips and then reinstall the front panel and cross sill. Expansion and contraction of the wood would be an issue.
Those might work, but you wouldn't be able to carry any sand in the bed. Unless your objective would be to spread that sand along the road. It would leak thru the cracks.

Mar-K has different options for the bed strips, including hidden fasteners. If you're looking to eliminate the bed strips altogether, you could fasten them with wood screws through the cross-sills from below, but you'd need some provision to allow the wood to expand and contract. It would likely expand and buckle or contract and crack. GM had a pretty good design for the wood installation in the first place. Many wood beds have lasted 60+ years.