My buddy has a panel truck and it has the original plywood bed with the bed strips on it. The older panels (not sure what years) had wood like the pickups, but there was an issue with exhaust fumes coming through the cracks.
BTW, there is no need to for creating any grooves in the plywood. The bed strips will lay flat on the plywood.
Carl

1952 5-window - return to "as built" condition | 1950 3100 with a 235 and a T-5 transmission