patagonian -
So what did I miss in my studies?
I can't answer that
But in a constant speed climb, Max rate of climb is purely rated to excess thrust.
Lift is less than weight in a climb.
Like trim set says - Take it to an extreme-
You are in a jet with buckets of thrust.
You are climbing vertically at a constant 120kts on the dial. The Lift component is 90 deg to thrust, and weight is directly opposite thrust.
Maximum ROC = Maximum excess thrust.