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I hope you can find somebody. Lots of shops don't want to install customer-supplied parts. They're concerned about warranty and also (probably mostly) loss of profit on the sale of the parts. But I think it's smart of you to find a good shop to do the work. From what I read, installing a new top on a vert is not a do-it-yourself job for anyone but the experienced.
I'm not a top installer by any means but I just want to let you know most places won't want to know you bringing in your own top.
Get a price on a new quality top installed, and then sell your top to a forum member who is capable of doing his own top.
Please don't let anyone talk you into the economy top, they only last about a year, then when you sell the car it will be like selling it as it needs a top, if it's a quality top you at least will get some of your money back.
Most places don't want to install someone else's top. Just about any competent auto upholstery shop can do a very good job. Make sure it's the cloth top NOT the vinyl. I'd call about 10 places and get estimates both with your top and theirs. While it is often true you get what you pay for, it's also true you can pay more for less. I've used Bell Upholstery, and Manny's Upholstery to do work for me over the years, they've done good work in the past. They are small shops in north Phoenix and fairly reasonable. I'd rate them as average.
Designer Imagines A Corvette That Looks More Like a Corvette Than the Corvette
Slideshow: A Jaguar designer's personal project imagines what a modern front-engined Corvette might look like if Chevrolet revisited the golden age of the Stingray.