Just a couple of cents from a virtual non-poster. I would definitely go for peace, and definitely try to get NY for it (which I has been said can be done). Though, what about trying to go for Seattle? Seattle is further from Washington, and so should be less culturally pressed than New York. I realize that getting New York would relieve the pressure on Chicago from New York, but you are trading cultural pressure on one city for pressure on another. Also, I think Philly is putting culture on Chicago, so it may be a trade for 2 cities that are culturally pressured.
If you can get Seattle, and I'm reading the map correctly, it's also more of a production center than New York, which should help with building units for the end of peace. I generally don't like to do it, but you might want to consider using stacks of workers to quickly bring online some improvements in San Francisco during a short peace.
I would also advise that you continue the war almost immediately after the 10 turns (if Washington doesn't do it for you). The way that I see this working is that if you can get enough units out to burn Buffalo, take NY and/or Philly, and defend against washington, you can then do another 10 turn peace to re-establish yourself.
If you do chose to go this route, I'd take some of the southern cities off of military production during the second war. Depending on the financial state of the empire, I would like to see a couple more workers come out of those southern cities (where it takes forever to get a unit to the front line). I'm seriously concerned about what you'll look like if you push too fast, manage through military tact to take everything of Washington's (take or burn), and then try to remain anything but easy pickings for the other continent. I would NOT say this game is lost though. From what I can surmise, you are probably producing about as much as Washington, and at a relative tech parity. I don't know what Cyrus or Hannibal think of Washington, but I can't imagine he has much to offer them. Once you get Washington out of the picture, you can worry mainly on your infrastructure, as the other continent worries about their issues.