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I dont know about the vette but I use Dash Topper in my Tacoma and it holds in place without velcro and is high quality. Of course the Tacoma doesn't launch like a C5.
You made me do a little search since I had thought about getting a cover. I looked at 2 and they both attach with Velcro. Sun will melt the adhesive. If you don't leave your car outside (like driving it) it would be OK. Maybe someone will give you a lead. I had run a trim shop once and can't think of any way to keep it in place on a C5.
I bought the dash cover offered by ZIP. It came with Velcro but I did not use to attach. I just lay on the dash and it does not come off even with the top down. But I always drive in the touring mode.
I have the carpet type with backing. Like all did not want to put Velcro stays in place just find. If it gets to windy I put pax window up
Thanks to all, who replied to my inquiry. Ordered the dash mat, last night. Hopefully it will stay put. At least it will stay put on those long hot sunny days at the car shows.