Pace,
Drag is made up of form drag, which increases as the square of velocity, and induced drag, which does indeed increase with angle of attack.
This is where we come up with the drag curve, where drag is minimum at a particular speed/angle of attack, and increases with EITHER an increase OR decrase in speed or angle of attack.
Vyse ("blue line" speed) is speed for maximum excess thrust on one engine, but is very close to the minimum drag speed. You are correct that drag from control inputs are a factor, but are included in the flight test data to determine Vyse.
By reducing the pitch you are reducing the drag and hence the aircraft will make the most of the available power and accelerate as it accelerates less rudder sticks out in the airstream.
Yes, but if you reduce "pitch" (I think you mean angle of attack- there is a difference) before you accelerate, you also reduce lift. If you were only maintaining height at Vyse, you are now descending. Sure you'll accelerate, but, as I said above, as you were at your minimum drag speed before, flying faster is only going to increase total drag and make things worse.
The blue radial is there for a reason. It really is the speed for best climb performance on one engine.I have a similar amount of light twin time as you (though a lot of years ago!) and I know that sometimes equates to "Not very much!!", but it is the best you are going to get. Fly any other speed, faster or slower, and you degrade the aircrafts climb performance.