600SS shock on Ebay
 

if memory serves me correctly these shocks are even longer than the shocks in a 900SSie which in turn are 5mm longer than the standard 600SS shock.
Which should make the shock in the Auction about 340mm, that should raise the rear if the spring isn't to soft.

http://cgi.ebay.co.uk/DUCATI-600SS-R...QQcmdZViewItem

What length are you running then skids ?

And what's the thinking on the best shock to run on a 583 SS anyway ?

I'm running a 335mm Hagon shock which is their standard replacement for the 750/900SSie, the extra 5mm in shock length over the standard 600SS shock coupled with the 1.7 to 1 rear suspension ratio gives a 8.5mm increase in rideheight at the back, also raises the exhaust and footrests slightly as well as steepening the rake slightly which in turn reduces trail to offer slightly quicker steering. Not sure how noticeable this is as I never got to ride my bike with the standard shock.

Well mate, if you've ever ridden a monster back2back with a std SS, you'll find out that std ss is slow steering !
my 620 monster has a raised rear ride, so i'm really expecting to notice a difference that will be too much to put up with, and would quite like to get another shock ready to try !
from what you say, just a decent ssi shock should be a good bet.