There are other threads that hit on this topic, or at least graze it.
Here's one example, and Tom (who started that thread) has some real-world observations from some other threads that inform a lot about chassis rigidity. That said, by far the two biggest issues are that nothing rigidly ties the front windshield frame to the B-pillar/hoop, and that the front suspension mounts are bolted to the frame rails where they are cantilevered several feet forward of any torsional stiffening areas (the firewall "frame" is the forwardmost). I think Tom identified that the rear frame behind the B-pillar is surprisingly flexible, too, even though it's a lot shorter than the front. The rear half of the floor across the passenger compartment is in fact steel. Adding to it and webbing the firewall would probably help torsional stiffness somewhat, but it wouldn't address either of the two big issues. A bolted in targa top helps a lot, but isn't as good as a welded or bonded web, or a T-top. There's a reason the Z06 version of the C5 and C6 have more or less permanently fixed roofs. Triangulating the front suspension area to the top of the firewall hoop would help, but that's hard. Same for triangulating the rear suspension points to the B-pillar. The Vette-2-Vette thing is just silly, demonstrating a massive misunderstanding of how torsional stiffness works. The damn frame rails are already about a foot tall, so adding a little extra beam structure with some light steel rods held in by heim joints isn't going to do ****.
The C5 still has a targa top, but it has some big advantages. It does in fact attach the tunnel to the frame rails near the firewall, so that helps. But it has frame rails hydroformed out of single pieces of tubular steel instead of stitch welding 14 pieces together. It also has a fully enclosed torque tube that ties the engine and transaxle together and is bolted to the frame, which adds a lot of stiffness. The C4 got no extra stiffness from it's C-beam: that only serves to control the engine/trans and rear diff from rotating around their later axes. Also, because the C5 used a transaxle, its front suspension mounting points are closer to the firewall and therefore they have less leverage on the frame rails. None of these are changes that can feasibly be added to the C4. It's possible that fully seam welding the entire frame would help. I know someone who may be putting that theory to the test soon.