8.75 would be fine to it's only a difference of 3 inches.. Are you going to do up lighting? In the second picture that ceiling is really set up for it and that opens up a lot of options on your finishes and textures on the ceiling.

Very pricey in many areas, and not necessarily an advantage. Hard to heat, cool, light and handle the extra-tall windows. 9-ft. is the added height norm, although one can always add additional volume with a peaked ceiling or similar.

I Understand. That's a common concern with my clients. But if you choose to have a 3-inch false ceiling, it will not kill the height. you need a minimum of 3 inches for the electrical conduits to pass. And as for the unhygienic environment, it is only created if you have a tray ceiling for cove light. If you install a plain ceiling after a thorough cleaning, there will be no hygiene problem. I hope this helps you all the best

Jaggi, while it depends on the overall depth of the coffer ceiling but as a thumb rule you can leave a safe gap/height of 9-9.5 ft from lower end to the floor. Thanks, Nitin Cornerstone Designs, Bangalore.