Just came back from a race weekend using a 110 Supercorsa front, 140 Rosso 2 rear tire, and the tires are great. Ran front 28psi on warmers, rear 26 psi. The Pirellis have really stiff carcasses and need lower tire pressures to get heat into them. It was a good combo on my 250 and its a great combo for the 390. So good, in fact, that I found out that the LH side t-rex case protector is touching down on the pavement as is the RH side Tyga belly pan edge.
I'd recommend raising the rear of the bike up 5-10mm higher than stock to get some clearance, which should also help with some front end feel that I was wrestling with in the beginning of the day. Wants to run wide on corner exit with stock geometry, so possibly raising the rear a little should help.