All good points, I am taking all of this into consideration. And those depths have been deepened 4'-6.5'.The problem with the pool built around the tree is not only will you get a LOT of debris in the pool, but if the tree is anywhere close to the size it is drawn as the pool build itself can very well damage the tree. Those roots are extending as far as the canopy. You'll be cutting into them.... so the tree might die from the damage anyway. How about an arbor in a position to help shade a specific area of the pool during the late afternoon?
I'd opt for removing the tree and enlarging the pool width. If you can lengthen it it will encourage more actual swimming. The baha shelf is taking up a lot of swim space.
I would also go with 4' as your minimum shallow end. Perhaps 4-5-4? That allows for sports & swimming without scraping knuckles. 3'6" is just too dang shallow.