I love trees and removing them unnecessarily is very painful and sad, but I recommend removal. You can always build shade from some sort of awning or even just sail shades, but the roots of the tree are going to give you headaches down the road, not to mention that the leaves and pecans will fall and make a huge mess in the pool. If it's just shade you're after you have far better options than the tree.
Steel done a week later, then gunite a week after that. I forgot to add it has pretty much been raining here constantly since December. And it always falls on the week days so nothing gets done. And on top of that the subs are always playing catch up. The last 6 weeks the place been a slurry of muddy gumbo clay and standing water.