>The force on me and on the kite is equal-and-opposite, but it was equal before I started reeling it in too.
Yeah, of course. The force is always equal when objects aren't accelerating, so when you reel in the kite at a constant speed with an increased force, the force on your ship is increased as well. When you reel in with more force you reel in faster, which means that you can make your increase in force arbitrarily small, but in doing so you'll make you're increase in speed arbitrarily small and make your reeling time arbitrarily large. In doing so, you'll end up accelerating the ship by the same amount.
The work done in reeling in the kite is obviously larger than the kinetic energy imparted on the ship and is minimised by reeling in the kite arbitrarily slowly. That energy doesn't just go into fluid interactions but also the potential energy of having your foil back at the ship as well as the ship's kinetic energy.
All of that is a bit of window dressing. To reel in your kite you need to increase the pull or force on its lines. That increase will equivalently act on the ship. The ship is being pulled a little bit stronger in the retraction process just like the original commenter asked.