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I think it is the same issue. The first thing I fixed on my '98 when I purchased it last fall. There are some good videos out there on the interweb to instruct you.
Different issues on mine. Sliding front to back is because of the worn out plastic washers as shown from link.
Mine rock because one of the support brackets are broken. Haven't had the time to replace it yet. Someone makes a replacement... sure it's listed somewhere here.
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.