How do I mitigate my convertible's annoying cowl shake? on 2000 Saab 9-3

I recently purchased this beautifully-maintained convertible having 116K on the odometer. The vehicle's only serious flaw is its lack of structural integrity manifasted by serious "cowl shake" experienced on all but smooth roads. I replaced all four shocks but have not felt any difference.

Asked by for the 2000 Saab 9-3
Any incomplete vehicle, without 'reinforcment', when subjected to lateral forces will exhibit "scuttle shake", sometimes called "cowl shake", depending on the geographical location and in this case due to the lack of torsional rigidity, ie steel top and/or rigid subframe. Inherent to later year model, 'unibody' covertible's. I do not know of a solution that will improve or eliminate this problem! However someone may. Different tires or tire size may help.
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seek a prof mech opinion in person as to what needs to be done