You can see how thin the inner skin is from the light on the outside shining thru. It's looking pretty good. It looks like the core was narrower than 1-5/8in. You will need to get a good idea of what thickness core if what I gave you is too thick. I've laminated transoms using 1/2in thick Coosa 26 by layering. Staggering the joints, and adding a layer of 1708 in between each core layer. Super Strong laminate was the result. Cut yourself a small piece of the 1-5/8in to use to measure you core opening. If it is too thick to use as the main core you can dig out that 2x4 cross brace and tablesaw the thick core material down to 2x4 blocks to replace the cross brace with. Don't leave the wood in the cross brace, replace as much of it as you can.