Hi bmi21,
I can’t find a reference for it, but from experience with an extended centreline your profile is based on you being on the centreline, abeam your present position, heading towards the runway.
The way to demonstrate it is to construct your predicted route when you are on an intercept heading (not good operational practice but will prove the point) and note your vertical deviation from the profile, then make your extended centreline and you will see that you are now higher on the profile than you were.
S & L