I am saving $600, before the transfer to Rome, by not flying into FCO, even if I took a flight with a layover. And I'd rather save that money and spend it on doing more in the country. I checked numerous times on numerous websites throughout the past few months. I will be flying Emirates in, which is pretty reliable. If I flew I'd have a 7 hour layover. Based on what everyone has said I think I will just take a train down to Rome since it is in fact cheaper and I can stop in Milan on the way instead of hanging out in the airport.
My international flight gets in at 12:15 into Milan; so, I could train to Milano Centrale, look around a bit and take a direct train to Rome.
On the way back though, I think I would rather fly. My MXP to JFK flight is at 4:30 pm. So I would take a 10 AM flight from Rome to Milan that gets in around 11:35, ideally. Four hours seems like ample time, even if there were say a 1.5 hr delay. Any experiences with Alitalia airlines? Are they known for delays? If so, then I suppose I could take a train back too.
Thanks so much for all the advice everyone.