Perhaps the thought should be : how do you best maintain a stabilized approach and airspeed, and then touch-down at the minimum ground speed. If that's the intent, then using full flaps in a strong headwind would not be a problem, if the wind is dead-nuts down the runway. I think this happens (20+ knots, dead down the runway) about 2% of the time, vs off by some degree, plus gusts, etc... So I always consider a strong landing wind to be other than optimal, and use no more than 2/3rd flaps, just to be safe. After all, there is no negative effect caused by decreased flaps into a strong head wind, because the goal is to touch down at a low ground speed, not a low air speed. You only want the airspeed to fly, not to drive
You could think of it like the strong wind is really a percentage of flap. It is giving you the same result, ie. keeping you flying at a lower ground speed, which is really the intent (touching down at a low ground speed).
So my plan has always been to use less flaps when it's windy, to avoid the possibility of having errant gusts push the plane around by it having excess body parts hanging out to catch the cross or gusty wind.
As a side issue, I wonder if there is a component of ground effect that makes a plane "float" when you have full flaps down, vs no flaps. Does it get "caught in the cup" vs flow smoothly under the wing. This would then be aggravated by increased wind speed.