HYGHFLY33
You are overcomplicating things.
The gradient required, whether it be climb or obstacle related doesn't change with wind.
It's just geometry in the case of obstacles and rules in a book for segmented take off flight path.
The gradient you will achieve when flying at a fixed IAS will vary with head or tail wind.
Therefore we calculate the gradient we can achieve in the actual wind (not really) conditions and confirm it is greater than that required.