4 hour uber ride to JFK

I am considering requesting an Uber from the Washington, DC area to JFK airport in New York, in a few weeks. (Yes, I know there are many other ways to make this trip; I will spare you the reason why I might Uber).,

My question is whether I am likely to be able to easily get a driver to accept this trip. Will the driver see my destination before s/he accepts the trip -- so the driver would only accept if the driver wants the trip?

I can understand why many drivers would not want this trip. But what I am hoping to avoid is a driver accepting, and then finding out the destination and fare and cancelling, and then the same thing happening over and over again -- and ultimately not getting a driver who wants the trip. If that is the likely result, then I will just find a different way to JFK, such as one-way car rental or flight etc.