SNS veterans posting above know that there's inherent flex to these cars. They were cheap and built to early 1960's build standards, and those standards didn't address this well enough for today. Crash test standards weren't in place, manufacturers didn't have to answer to much litigation in this regard, but we all know how that changed before the decade was out.
What to do? There's no free lunch. Guys love these cars because a small block is a drop in, but these bodies end up cracking, flexing, breaking and handling poorly when there's a lot of power under the hood and traction upgrades are made to go faster in a straight line. Addressing the problems adds weight. Sub frame connectors are a start. A cage integrated with the front and rear subframes is another good step, but probably not enough. There's a huge call for body 'drop-on' subframes that will be able to hold all of the suspension and driveline, but now you're adding significant weight and there's no test data that that added frame or roll cage will make the cars significantly safer to occupants in a collision, though they should. Any of these upgrades should be accompanied by safer seating, seat to body attachment, restraints and other improvements as well if that's the goal of the modification.
Guys upgrading Novas are asking a lot out of early '60's practice of the art car building design, especially from a model designed to be light and cheap with no waste. GM wasn't trying to compete in today's market or even today's hobbyist market with this car.