More pictures would be helpful in this application.
Regardless of the current state, you have an opportunity to get it don right this time.
Given the climate in your region and the relatively small insulation depth in those cathedral sections, I would suggest that try to do some reading on your options.
You might be well served to contract with a building efficiency professional as well so that he can help coordinate your efforts.
BSC Roof Design
I am sorry you are getting such bad contractors out there.