If you do any mods that lessen chassis stiffness ( ie .. cut holes ,remove reinforcements etc ) it will make the car more flexible which coverts already have an issue with . Although they are boxed front and rear having no roof really comprimises the chassis stiffnes.
The worst I ever experienced was a new 1992 Olds Cutlass covertable... if you drove over railroad tracks you could feel the car flex like a wet noodle ! I sold them new and once had a middle age woman ask me " Did this car just move ? " lol.. I said "yes maam it did ..."