Hatch Revamp

I am revamping my hatch. The struts were stressing the latch and wrecking the wood where they attached. Took those off along with the plywood on the inside. Going to go with poles to hold the hatch up.
The hatch fits much better on the body but now I am getting quite a bit of flex from the hatch. I reinforced the corners with metal angles. I also revealed the builder used 2 pieces of plywood to shape the skin and there is a seam down the middle of the hatch. The formica covers the seam but....
I thought I would cut and glue the old plywood back into the cross beam sections of the hatch to reinforce the seam and the hatch as a whole. Hopefully that will lessen the flex too. I do want to leave the cross beams exposed.
Thoughts or other solutions?
RRRL
The hatch fits much better on the body but now I am getting quite a bit of flex from the hatch. I reinforced the corners with metal angles. I also revealed the builder used 2 pieces of plywood to shape the skin and there is a seam down the middle of the hatch. The formica covers the seam but....

I thought I would cut and glue the old plywood back into the cross beam sections of the hatch to reinforce the seam and the hatch as a whole. Hopefully that will lessen the flex too. I do want to leave the cross beams exposed.
Thoughts or other solutions?
RRRL