An airplane cannot climb while stalled--I know--I've tried!
Best rate of climb is not necessarily the best climbing airspeed, if you know what I mean (and I ain't REAL sure that I do!) Rather, the rate of ascent, as you note, may not be the fastest the machine can go with the nose pointed above the horizon. Like every other maneuver, it's a compromise. Presumably what you want is best SUSTAINED rate of climb.
Haven't run across any web sites that address the matter.