I do not think four separate pieces will work as described. If you want to go "wall to wall" and get the most penske you can get stuffed in the cavity why not two 3/4" pieces each cut in two pieces. The inside piece cut 1' from the left and the outside piece 1' from the right. You could then work each layer in as tight as possible still giving you a solid 1 1/2" with no seam in the middle of the transom. Each seam would still have a solid backing of 3/4" penske. Make sense? It will take a lot to trimming and dry fitting to get just right but it would still be as strong as you would ever need.
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