Thank you all, indeed my chances of an upgrade are minimal as I'm a BA card holder. The price in economy seems a bargain to me right now ... they're quoting me USD 680 (Eur 550) for a trip from MXP to LAX and back via LHR/CLT and JFK/LHR on the way back.
Considering it's mid-July (17 Jul - 1 August) is sounds a good price to me, isn't it?
I normally go for J on long haul but I can't really justify the difference in price this time (J is around $3000).