AA, DL & Emirates have been having fare sales between JFK-MXP. UA might have deals as well out of EWR. Not sure that I would chance it and risk missing a cruise unless you give yourself at least a week to get there and plan on several backups.

That said, a few years ago, I once got to FCO on AA in J only because a thunderstorm passing thru the area caused a number of diversions and opened up a bunch of seats. I was resigned to settling in a middle seat in the back for 8 hours. The FCO flight left on time. For the return, MXP & FCO were both oversold so we ended up taking the train from MXP to ZRH to fly back. This was in October.