I know that this is going to get a bit more technical but believe that I can tell you that you are wrong on both assumptions.

A chart referred to as a polar plot can be generated for a boat. It indicates where optimum VMG (velocity made good) is made for a particular craft. This is the point where the tradeoff from footing for increased speed balances against the increased distance travelled. In your example, the higher a boat sails the slower it goes. True and therefore the slower the fluid flow over the foils. This potentially means more leeway. The boat is pointing higher but the course isn't.

In regards to the headed tack, the tactics vary depending on if its an oscillating or persistent shift.