Flying non-rev to Italy

This will be my third trip to Italy on a Delta
Friends and Family pass since July, 2001, so I know I have to be flexible. And I'm thinking of going either in the fall or next spring, so this is fairly theoretical. What I'd like to know is whether I'd have a better chance of making a flight if I departed the U.S. from New York rather than Atlanta?

My first two trips were late July departure/August return and late May departure/June return. On this trip I want to go in either the shoulder of the season or off season. I'm wondering whether, if I didn' t make a flight for Rome or Milan, airport listing for London and flying something like Ryanair to Rome Ciampino, might not be a good strategy. Any thoughts?

I travel alone, the pass comes from my cousin's wife who's retired. She does have a lot of seniority.