Early-A Convertible Chassis Reinforcement

Before totally rebuilding the suspension and steering, and soundproofing my '64 Valiant convertible, there was enough slop in everything to absorb any chassis movement, or at least to make it unnoticeable. Now the car is quiet and tight and chassis flex has become obvious.

Has anyone reinforced the frame on an early-A convertible? If so, what were the results and what would you recommend?