Mike welcome to TFP, great design video. Here is a couple of thoughts.
Hip, Gable, Mansard??? This is a personal preference. The wife and I chose Mansard and our roof is 12 feet high. I think the Mansard style is easier to replace screens however we have had no experience with Gable or Hip.
8 feet walls are plenty, ours measure about 7.5ft high and we are pretty happy with that height.
1. Speaking from experience if you are putting in a pool cage. Put in a double door on one of the sides. I only had one door and ended up putting in a double door and another single door on the opposite side. I should have listened to my wife
2. Plan on plumbing electrical and water for a future summer kitchen.
3. Plan on adding solar and heat pump in your equipment pad.
4. Make sure that you have a very large equipment pad, our equipment pad is 19 ft long x 9 ft wide.
5. Put lights at pool equipment pad.
6. Put in water spigots in all 4 corners of the screen cage both inside and outside the screen cage.
7. Put in electrical outlets in all 4 corners of the screen cage both inside and outside the screen cage.
8. Go with a large outdoor space as possible. We have 1800sq ft of pavers and we wish we did a larger space. You will be quite surprised how much room tables chairs and lounges take up.
9. Run conduits for speaker wires if you plan on wired speakers.
10. Plan on positioning your pool so that you can watch TV comfortably when you are in it. I know that this may sound strange but we love watching TV, football games, NASCAR races and movies when we are relaxing in the pool.
11. Place pool light facing away from the house, we had ours facing towards the house and we notice some glare from it.
Look at the 3 links in my signature bar for ideas. Post lots of pics