We already have ships that require no power, and merely utilize existing air currents. They’re called gliders.
So if we had an antigravity airsailing ship it would probably be designed like a glider except you use the antigrav to attain height rather than being towed by a powered plane.
So you turn on the antigrav and rise up to your preferred height, then turn off the antigrav and convert the potential energy you gained into kinetic energy. The only problem is that now you’ve got a perpetual motion machine unless your antigrav requires power, and if it requires power you might as well put a motor on your airship.
How about, you use a tether to lift your ship from the ground, like a kite? And once you’re high enough, you let go of the tether and operate like a glider? That way you don’t have to turn antigrav on or off.
Thinking about it some more, the more ridiculously big you make it, the worse it will do.
I’m having trouble wrapping my mind around the concept of sailing close-hauled. But beam reach (90 degrees from wind) is easier to conceptualize. A ridiculously big keel becomes a ridiculously big sail, and you’d be pushed downwind even harder. The only way it would work is if the boat is already in motion, and it would have to be going faster than windspeed to do any good. And the lift created by the sail could never match that.
The only way I can thing of this working is that the keel would have to be ridiculously big, and the sail ridiculously bigger – enough so the keel is in thicker atmosphere than the sail is. We’re talking about a boat several miles tall.
Actually, we already have vehicles that do this, except they work underwater. The glider adjusts its buoyancy, equivalent to using antigrav. When the net weight points down, it glides down. When the net weight points up, it glides up. Yes, it takes a power source to change the vehicle’s buoyancy, but the energy/power requirements to do that are much smaller than that needed to push it forward via rotors.
Physics supports the possibility of doing the same thing in air, but the engineering challenge is much greater.