Bear in mind that while Switzerland has chosen to adopt EC 261/2004, it is not bound by the decisions of the ECJ's expansive reading of the Regulation because Switzerland is not an EU Member State.
You have essentially been told that the "boarding chaos" at FCO was an "extraordinary circumstance" and that the delay it caused is not subject to delay compensation. That seems in line with a rational reading of the original Regulation without the window dressing of the ECJ. You were nonetheless due a duty of care which ought to have included transport from JFK to EWR as EWR, not JFK was your final ticketed destination. To me, this latter issue is not worth fighting about as the three train combination from JFK to EWR runs about EUR 10 in total. You could submit those receipts nonetheless.