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I can't comment on the shallowest, but both Pioneer and Kenwood units will fit without sticking out if you're willing to cut off the plastic 'centering hole' that the oem radio uses. Aftermarket HU's don't need that bracket, and the oem radio is also fine without it if you ever want to return the car to stock.
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.