You might be surprised at how much stiffness that hump adds.
Years ago i restored a Falcon Sprint convertible. As that was a unibody car, and relied on the top for strength, making it into a convertible was a challenge. The engineers beefed up the rocker panels, making them into tube structures that carried the loads between the front and rear suspension mounting points. It worked well enough. The one O had was so rusty that the rocker panels were completely rusted away. the ONLY thing that kept the car from folding in half was that driveline tunnel.--at least until I replaced the rockers with some I had made up out of 12 ga. THEN it was stiff!

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1982 300SD " Wotan" ..On the road as of Jan 8, 2007 with Historic Tags