You might want to look a little closer and the airlines mentioned above. Turkish Airlines takes between 28 and 36 hours to get to Rome. United flies to Rome in 12-14 hrs. for about $223 more. London to Chicago takes Turkish Airlines between 25 and 31 hours to get to Chicago. United flies it in 9 hours.
Lot flies to Rome in 15 hours and back from London in 13 hours, but you'd only save $30 over United.
Often, the lowest price is not your best value in airfares.
I don't know your groups' itinerary, but have you considered reversing your route--into London and out of Rome? I was thinking Heathrow had very high taxes on flights leaving there for the U.S. You might save there.
2014 prices are again expected to be high due to 3 airline affiliations controlling the market to and from Europe. Prices are the cheapest Tuesday-Wednesday, and Spring airfares rise substantially on 3/28/2014.
When I'm looking to fly anywhere, I look at flights every few days @ http://matrix.itasoftware.com I'm trying to get a baseline price, and watch for any changes/trends. I recently bought a 3/25/2014 open jaw airfare on a one day sale to Budapest and home from Prague for $728. The flight has been running $1,050. Today, the airfare dropped to $835-863, so this would be a good day to buy.
I would suggest you watching your planned flight dates and airfares for a few weeks. After the Christmas Holidays and the first of the year, there's a good chance that more one day sales will be posted.