"Doesn't going faster make your apparent wind direction change to more on the nose? This would mean the faster you go, the less high you can point - right? "

Right, and wrong too. Sailing theory is quite diverse, and contradicts itself sometimes. By footing off & going for speed, you load up the centreboards which gives you drive to windward, so although you are footing off you are actually pointing higher than someone who is pinching & going slow. His heading may be higher than yours, but becuase he isn`t loading up the foils, he will be slipping sideways. You`ll get there first.

Cheers
Steve