The only nonstops today seems to be on ITA.
There's a 9:40am flight and 12:25pm FCO to JFK
AA has a flight from London to EWR at 7:10 pm landing 10:00
there are several flights FCO to LHR over the day.
Others also have connecting flights. In order of departure:
Delta 9:20am
United 9:20am
Turkish 11:20am
United, BA 11:30am
Air Canada 11:30am
etc
Of course the prices are ridiculous, but maybe you can get AA to put you on something sooner.