I recently found two award tickets MIA-ZRH on Swiss (using United points). Return is on Virgin Atlantic LHR-MIA. All tickets are business class. I actually found it easier to get the tickets out of MIA than I did ex NYC.
That being said anything in reward tickets to Italy is a tough find since there FCO or MXP isn't really a transit hub like FRA LHR CDG - there just isn't that many aircraft going to those airports, that means less "free" seats
You will have to look everyday at 330 days to find something and it may not be available. Think of going MCO/MIA to LHR via Virgin. The redemption rates are lower than most (although that is offset by high fuel taxes). After that fly to wherever you want to go to
also look for low priced business seats at the same time. Some can be competitive