From the sounds of the description of your cage, it is not NHRA legal for an OEM frame car. It sounds like that the rear end is flexing the rear of the frame enough to wrinkle the quarter panel. Since your cage is only welded to plates in the trunk floor the cage is not stiffening the frame, which is allowing the body to flex.
Here is a link to a NHRA tech page.
http://www.nhra.com/contacts/tech_faq.html
Note that in both diagrams it states that all cars with an OEM frame must have the cage welded to the frame. I think I'd have a talk with my cage builder. 
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6APPEAL
87 GN - street machine
87 GN # 2- TSM wanna be
00 GSE - wife's black, forced induction car
05 Chevy 2500HD Crew- it's black and turboed
Looking for another Buick - 70-72 GS/Skylark convertible or 65-72 Sportwagon
85 T-Type - white, the anti-GN - Sold
86 GN - totaled with 88k miles in 2003 
86 T-Type - Sold
78 Regal Sport Coupe - The one that started the boost addiction - Sold 
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