In reference to your arbor/pergola there are other ways to determine the amount of shade achieved. I would ask my customer at what time of the day they want shade the most, early in the morning and late in the afternoon, or at noon. If they want more protection at noon you would want to run your materials east - west, if they want more coverage for early morning and late afternoon run your materials north-south. Also what season are you building this in because the sun location varies with the season and the geography.
Now there are variables on the spacing of your materials. some people set their joist at various spacing's, the closer together, say 16 inch on center, gives a lot more shade and that again depends on what size boards you are using, the higher the profile the greater the shade. Now lets talk lath or slats for the top most people around here use 2x2's for lath the question is how far apart do you space them, the closer more shade, the further away you just get the look of an arbor/pergola.
You may want to use 2x4's on edge much more shade based on how far apart they are spaced.
These are all things you need to discuss with your customers explaining the differences and the benefits. You would be surprised how many people have no idea what goes into getting the correct product for their money.
As far as the height goes you said the soffit is 8'6", correct? I would build above the soffit, presuming your project is free standing, I always figure the bottom of the beam to be 8 to 9 foot high. Most people want to be able to install ceiling fans underneath to give a comfortable breeze. Make sure your customers know that they will need to make sure they are buying a ceiling fan rated "WET".
By the way my advise on the purchase of a ceiling fan is let your customer provide it to you, not you go out and buy it for them. I made that mistake once it turned out to be the wrong color, wrong light kit, wrong size, and the blades were not the right shape, lesson learned.
Thanks for the opportunity for me to be able to give back.
I think I exceeded the quick reply here.
Bob