I'm not forgetting...I disagree. In my experience if the apparent wind is forward of the beam, then it moves farther forward and increases as boat speed increases. If the apparent wind is abaft the beam, it moves aft and decreases as boat speed increases. In either case, I have to adjust my sails as the changes occur.
My boat can't see true wind...it only sees the net effect of true wind, set and drift, leeway, which manifests as apparent wind. True wind obviously has an effect, and has to be considered to determine your heading, taking into acount the boat's sailing characteristics, current, obstacles, crew comfort, waves, etc.
I always trim my sails to apparent wind. What other methods are there?
I do agree that boat speed can improve you pointing ability because of lift from the keel and rudder. That may account for your decreased angle as speed increases. When you are going from 44deg to 36deg in relation to true wind as true wind increases, how is your apparent wind affected?