I was a bit bored last night, so I started browsing through AY's offer pages for different countries and I'm glad I did. NRT was cheapest ex-Italy, and instead of BUD, which I don't like very much, I'm now flying out of MXP and into FCO, spending an enjoyable weekend in both MIL and ROM, all-in for €80 less than BUD would have been. ^ I class to NRT was €2139 which I consider a good price. I had to book over the phone because, unsurprisingly, the website couldn't sell me a ticket this complicated: open jaw from Italy to Japan, with stopovers at HEL both ways. No extra fees for the phone booking, though. ^
Also booked NRT-GUM on the JAL website. Must have been the longest booking process I've ever seen, but in the end I even managed to select seats both ways on the second try. (I checked award seats via BA, too, but there was little availability. Would have been a bargain at 20.000 Avios return instead of the €514 I now paid for L&S class.)