I'll say it again, the CP means nada, squat, Jack, zero, nil, and completely unnecessary for pivoting purposes. I'm starting to feel like John Cleese trying to return a dead parrot. The CP does have beautiful plumage for other styles of shooting though.
I didn't get into the details of your pivot triangle method. If that method makes use of a line from the pocket through the object ball then I think we're talking about the same thing. I think the words "contact point" might be a matter of semantics. If your PT uses the angle between the pocket, ob and cb and then makes some adjustments to put the cue on the shot line then we are pretty much talking about the same thing, which I can live with.
And now for something completely different... these guys have nothing on these aiming forums:
https://youtu.be/kQFKtI6gn9Y