Sure G, to summarise..
How to TEST, as opposed to simply dismiss/deride - based on dogmatic 'knowing'..
The effect of head wind on climb rate..
A heavier than air - aircraft - has to generate thrust, for lift- in order to climb..
The greater the level of thrust - over drag - & > lift - the quicker the climb..
Climb rate is matter of lift produced - via Angle of Attack/speed..
You are an S.S. fan G, so you get that the S.S. has such an excess of thrust over drag that it don't need aero lift at all..
Planes however do, & air-speed is airspeed over a wing..& dependent on thrust being provided..
More thrust can overcome AoA induced drag & maintain a higher angle..
Which - for a given speed - will allow quicker climb rate & a faster time-to-climb..
& more speed - at original, lesser AoA will too..
So will headwind induced 'free' airspeed come into play?
A valid scientific test will settle the question, & ranting dogma wont..