Rose,
thanks for your feedback.
We are set on the whole roof concept. We get a lot of snow here and want to keep the future birds nice and dry. Additionally, we get a lot of wild birds that love to drop bombs everywhere they find a place to perch. Having a roof partially covered with hardware mesh /wire incentivize them to use another perching area. I have reached out to engineers (Angis list) to get quotes for the engineer design. Also, a couple of lumber businesses have sent me the design and price for the trusses which are one of the main components of the covered run.
thanks again