...Why assume the Yorktown
would be in interstellar space, though?
manufacture hundreds of square kilometers of solar sail
One might suppose that future technologies capable of creating this surface area would also result in it being stowable. That is, the sail would be sitting in some corner of a cargo hold, in a cube measuring about two meters per side, and just waiting to be thrown overboard and pumped up with electric charge to force a neat and tidy unfold.