Jetpipe.
I am afraid your logic is very flawed. Your calculations are correct, and yes, relative to the air TAS is the correct speed to use. However, the whole reason for having climb gradients is to make sure you can comply with ATC requirements and obstacle clearances. For this, what you do relative to the air does not matter, it is what you do relative to the ground, and therefore, we must use GS and not TAS.
Using ground speed will allow us to figure out what kind of ROC we need to for example clear a mountain top.
I cannot find a better way to explain this, and have to say I am a bit puzzled that some people apparently do not grasp this. It is basically just the fact that we need to establish a certain gradient over the terrain, and not relative to the air, because mountains do not move relative to the air, they are fixed to the ground, and therefore we must also think and make our calculations relative to the ground by using ground speed.