Guess I had a different aero course and pilot training courses than those here.
I can't find a single reference to the effect that we must increase lift to climb, with the notable exception of being so far behind the "power curve" that we are virtually stalling.
See:
http://www.dept.aoe.vt.edu/~lutze/AOE3104/climb.pdf
See also discussions right here on pPrune forums:
BEST ANGLE vs BEST RATE of climb [Archive] - PPRuNe Forums
So I stand behind the Vermont aero department statement referenced above:
13. Climbing Flight
In order to increase altitude, we must add energy to the aircraft. We can do this by increasing the thrust or power available. If we do that, one of three things can happen:
1. We will increase kinetic energy (accelerate).
2. We will increase potential energy (climb).
3. We will do both, accelerate and climb.
If we desire to climb, we should hold the airspeed constant and use all excess power to increase our potential energy.
Further, as Nuts pointed out, at an attitude of 17.5 degrees +/-, a significant amount of thrust should contribute to a climb. No need to increase the trimmed AoA or even the negligible amount of gee command to the 'bus computers.
Doggone it, the guy was behind "the curve" at his power setting - no climb capability without more thrust, and it appears he had plenty but got it applied way too late.