HI walter. It's dumb for me to give advice about another city than my own. But are you sure you are doing a sufficiently sophisticated search? Are you using a wide ranging site like Kayak or Google Flights? Are you using your favorite "real" airline site? Are you using a "bargain" airline site?
It makes a big difference. If the $200 is a big factor for you, I suggest you look into flying from Philadelphia or Newark, as well as from DC. You might even save money by flying to the hub of an airline you don't usually use, like DC-Chicago-Venice. From NYC, it seems to me like the there are more Venice flights every year. Yes, some of them may be summer-only.
My wife and I have often saved money by buying a Lufthansa flight through ANY of their hubs in Germany, and then their local flight to our real destination. Since you can't get your hotel room at 7AM, we don't mind arriving at noon!
Just another idea for you, I hope.