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I bought a "Topstopper" somewhere on the web. It is a simple little rubber covered piece of 1 x 2 that holds the convertible top up while I dig through my 80 different car care products and car cover for my wife's always elusive hat.
It is great. Cost $20 delivered, but you could make one for $5 pretty easy. $2 if you have that tool dip stuff already.
Anyway, it is a pleasure to use. I think Corvette Central has a more perm one of steel, but I don't know what is involved in installing it. This piece you just stick on top and throw it onto the junk when you close the back, it is right there next time. You won't want to ever reach in the back without sticking it in first! Best $20 I've spent.