I'm curious about your statement about "stock C5s...even FRCs/Z06es" lacking "lateral stiffness". There is no such term so maybe you mean stiffness in torsion or twisting. If that's the case, when you say the car lacks torsional rigidity, can you quantify that in some way? Have you tested the car's structure? If so, what is the stiffness of the car in torsion and, since you say it lacks stiffness, what is your benchmark for a car which has adequate stiffness?
As for the "chassis groan". I also own a 2004. I've driven it at an angle, across sloped driveways which are so steep the car will lift a wheel off the ground and my chassis doesn't make noise. Perhaps this groan you hear is not really a rigidity problem but a case of something loose or rubbing somewhere.
As for the console temperature issue, there is no question that a thermally-coated close-out plate will provide a reduction in temperature. Of course, you can also add thermal insulation on the bottom of the existing plate and achieve the same result for a lot less money, but...I digress.
What I'm really interested in is some kind of understanding, from an objective standpoint, if your belief that the C5 structure is weak in torsional rigidity.