hello crash and welcome--you have found the right place for help, advice, rideouts, and everything else that you need ducati wise!!!!
i have a 600 with exactly the same problem. i have stripped the carbs and balanced them searched for air leaks changed the throttle cables etc but it has made no difference- the problem only seems to occur after a more spirited ride as frank mentions it may be that the engine/carbs getting hot- mine settles down after about 15 seconds anyway so i have learnt to live with it and dont worry about it any more--
As DC says see if you can make it to a DD round well worth seeing these little ducatis getting thrashed,er, i mean raced around the track
but be care full where you leave yer bike
As you are up at the virtual bar i'll join you in an ice cold Tooheys New(i wish)
Dave