Congratulations on trying to land every booster. The lessons learned will be invaluable in space. An congratulations on posting the failures as well as the successes on your site. Thanks for the video, for your observations, and for your humor.
You are right comparing the problem to landing on a carrier. If you would allow a few observations from a pilot, here goes:
As you say, the barge is translating and rotating. The rotation is in three axes: pitch and roll as well as yaw. After touchdown the tail of the booster is effectively fixed to the barge, but the nose (because of the pitch and roll of the barge) must describe an ellipse. Somehow forces must be generated to a) accelerate the nose around the ellipse, and b) counteract gravity (because the long axis of the booster is not parallel to the gravity vector), and c) compensate for the moment of the long axis if there is any translation at touchdown. Forces a, b and c act in the same direction, so the force required can be as large as their sum. The required correcting forces can be a) transmitted through the landing legs, or b) generated by the nose thrusters, or both.
In the video I can’t see the nose thrusters (last time, in the Atlantic, I could), nor do I know their thrust. However, you should be able to calculate the maximum size of the nose ellipse, as well as the maximum lateral velocity at touchdown, with the thrust available from the nose thrusters.
Last time I wrote I also suggested that the nose ellipse be flown prior to touchdown, to minimize these forces at touchdown. Also, a little more time in the vertical deceleration schedule might be advantageous, especially in the last ten meters or so (if the video is in real time).
The carrier landing analogy, then, is interesting but incomplete. The pilot of an F-18 can, for all practical purposes, consider his aircraft (and himself) as one mass acting at their combined center of gravity. The booster – a long shape touching down on its tail – cannot.
I wish you and your ventures well. No – more than that. They are our future.