Your bike is fuel injected so the lever on the left hand bar is a fast idle control rather than a choke. My guess would be that one of the sensors in the injection circuit has failed, possibly the one for the outside air temp so the bike always thinks its cold and richens up the mixture as it would do for a cold start. It needs plugging into a Ducati Methesis tester which will test all the injection components and tell you which one isnt working.
Its worth you ringing Neil at
www.cornerspeed.co.uk (he's near J28 on the M1) but he gives free advice! He wont rip you off with randon "inspection" charges either. Might be a bit of a trip for you but i know quite a few guys who take their Ducatis all the way from London for him to look at.
Tell him Paul sent you as well.