Impossible for anyone to tell from your info. Basically, what?

Less than 3 years of trying to heat and cool a double height room unsuccessfully, that's for sure. Especially if it's a new build and not a retrofit.

I agree the heating and cooling of double height rooms is high.

The statements about heating and cooling are too general, it really depends. My house with double height living with a southern exposure in Texas maintains a reasonably cool temperature with solar shades. But my previous house same area and one story was much warmer. But, that is not what you are asking, sounds like a new build?

Waaaaaaaay to vague. New build? Retro-fit? What are you working with to start?

But if you wanted a ridiculously rough estimate just to get the vaguest of ballpark ideas try $200 per square foot.