The 3/4 and tonner bed is basically the same from 38 to 52. There is a nice thread over on the Ford Truck Enthusiast site of a complete restoration on an F-2. There are lots of pictures in that thread including at least one showing the cross members, post here:
https://www.ford-trucks.com/forums/1...l#post19702293.
As others have stated those among us who are less talented at woodworking can purchase from Bruce Horkey, link here:
https://horkeyswoodandparts.com/page29.php#woodcross. Given your woodworking capability you won't need to do that, but the picture might help.
I have saved a few pictures of original 3/4 / tonner and F-2 / F-3 beds with good condition original appearing bed wood, notice the welting along the edge of the bed wood between the outer board and the bed side.
