Sorry about the chip...but I can't concieve how this would have happened from taking the badge off. If you can somehow send a close-up picture I could advise better (regarding having the body shop fix it), but since your initial problem was that it was cooked, just put another one on - only straight this time.
Also, did you already get the residue off? Getting residue from double-sided tape depends on many factors...such as how long it has been there, the type of tape, and the thickness of the remaining residue. For instance, I just tore off my paneling on my Landcruiser to have them repainted, and the reside was horrendous to remove. After spending a couple hours and trying 4 different solvents, I elected to borrow my buddies air-powered rubber wheel - I don't know it's official name, but it is like a giant pencil eraser that acts like a rubber grinder that doesn't damage the paint at all. This made the job easy - it's great for removing pen-striping and all sorts of adhesive left-overs.
Also, did you already get the residue off? Getting residue from double-sided tape depends on many factors...such as how long it has been there, the type of tape, and the thickness of the remaining residue. For instance, I just tore off my paneling on my Landcruiser to have them repainted, and the reside was horrendous to remove. After spending a couple hours and trying 4 different solvents, I elected to borrow my buddies air-powered rubber wheel - I don't know it's official name, but it is like a giant pencil eraser that acts like a rubber grinder that doesn't damage the paint at all. This made the job easy - it's great for removing pen-striping and all sorts of adhesive left-overs.