I would start with DL thru JFK. At Zed Low, it's probably the cheapest routing all on one airline. If she substitutes in Jetblue on the SEA-JFK segment it gets even cheaper. It looks like 2 DL flights from JFK-FCO, a 763 and 764 that evening.

She can price out all the options if she clicks on the ID90.com link in Alaskasworld. It's a great pricing tool.