This was from 2011, when we went to Boston. The thin red line highlighted by blue was our actual track, and I plotted a course to overlay it so the program would display the approximate course heading lines. Note that our COG was tacking through about 110-degrees (108 starboard; 114 port) and I wasn't trying to pinch, but my compass would have led me to believe I was tacking through about 90-degrees. The difference is leeway. (BTW ignore the speed that shows in the chart -- that was the planning speed for the route).

I picked CC Bay because current isn't much of a factor. Tacking against the current (or with it) can change things dramatically.

Also, to confirm your question -- yes apparent wind moves further forward as the boat speed approaches (or exceeds) true wind speed. We're close hauled most of the time when reaching.