I have a few general tips, I have taken flights with similar times to yours.
Start living on Italian time once you get checked in to the airport, if not before. So it's 1PM in DC? No, it's 7 in Italy. Mentally call your lunch dinner. Eat in JFK if you're hungry then try to sleep as soon as you can on your JFK-Venice flight. 8:30PM is 2:30AM and you should be asleep! Never think about what time it is at home until it's absolutely necessary (calling someone, business hours). You are in Italy once you get to the airport. I think the mindset is a big part.
Stay hydrated and don't drink alcohol on the plane or the airport. Alcohol makes you tired, and the last thing you need is another reason to be tired.
But arrival day will be tiring nonetheless. Don't plan anything difficult but be sure to be outside, in the sun - drop your bags at the hotel, go for a walk, enjoy the ambiance, get coffee. Walk, get sunshine. Eat lunch when you arrive in the city. Take a short nap when you can get into your room (so nap 3-4 or something) then be sure to go back out no matter what. Going to bed for the night at 4 is not going to help anything. Eat dinner, go to bed anytime after 9PM. Get up at normal time the next morning.
My worst jet lag was when my plane arrived in Madrid at 5AM. In Spain at that time of year (fall), sunrise wasn't until 8 or so. So those3 hours of wandering around in the quiet dark was killer. Your 11 AM arrival is helpful in this way.