Thanks all for the tips and suggestions. I ended up not driving it and things turned out okay, car should be ready by Tuesday. The weird suspension/shock issues I noticed were apparently caused by the right muffler being shoved under and into the shocks.
They (Progressive) are having to replace the rear bumper, some sort of rear bracing thing and the mounting for the front license plate. All totaling roughly $3,100 US. Thank god for insurance! It also looks like the cops found the guy behind me at fault and his insurance will take care of my deductable and everything.
I have to say I am very impressed with how the Edge handled everything (compared to the other guys car) and how well Progressive is doing as an insurance company.