Costs can greatly vary state to state or even area to area, depending upon the economy, availability of materials, labor costs, size of the structure, etc. This was built in the San Francisco Bay Area, one of the most expensive areas for real estate and construction costs. The arbor structure alone cost about $175/sf about 2 years ago, not including the heaters, lighting, and modifications to the house to accommodate it.
In regards to your house builder, it is unfortunate that you feel that you are in a situation where inflexibility exists. Any architect, contractor or consultant should recognize that the homeowner is the one who will be living in the home for years to come and is paying all the expenses. I suggest resolving these issues so that you can achieve your desires. Sometimes an architect or designer can act as an intermediary and assist in resolving constructibility issues.

Thank you VERY much for your fast, detailed and thoughtful answer. We are currently looking to work with this group/ residence 3 where we want to move the back wall out to be even with the nook wall. We would then use your solution above to extend a covered patio (necessary here in AZ). http://www.theopencollection.com/residences/ I wish the builder saw things as you eloquently stated them above. I *think* I am the customer....but do not always feel like it. :)

Again, thank you VERY much for the time.

I love this design and am about to copy it. i want to have daylight come through and am curious what material did you use for the roof?

It is a material called Polycarbonate. If interested you can click on the 'more info' and find out more details about this project.