Steve, you're in building climate zones 2, 3 or 4 depending on what county you are in....click on the map to see the requirements:
https://energycode.pnl.gov/EnergyCodeReqs/?state=Georgia
https://law.resource.org/pub/us/code/safety.html
It appears your state has adopted
energy code 2009 IECC which dictates
alot as you can see to satisfy building permits. Strawbale code is in 2015. Before you get too far along you may want to check with your building and safety office. In code you'll also find vapor barrier and retarder requirements for the walls, roof, floor, that do not work with strawbales, natural floors, roofs, etc....bale code makes it easier.
R-45 is optimistic for SB walls, more like R-30ish depending on density and straw direction. R-45 sounds reasonable for Z-4 roof, but be aware blown in cellulose settles and looses whole r-value. The main purpose of the gap (3/8 min) under roof cladding is vapor control and drive by pressure and temperature differentials, house wraps, water and ice, do not leave
enough of a drain plane and can cause heat and condensation build-up, so water gets trapped against sheathing/claddiing that can drive to the interior through holes, rot structure and cause mold health issues. Whether it aids in "cooling" will depend on the time of year, materials and design of your vaulted roof......The interior material coupled to indoor air, and in some cases isolated/insulated from the exterior, sun orientation, has the most profound effect on cooling and heating loads, clay and lime plasters,
wood, would be good examples. R-value does not mean as much with them, but unfortunately the inspector that probably does not understand has to be satisfied, or you hire an Engineer to stamp drawing's which may be hard to find too.
Don't mean to rain on your parade, but unfortunately those are the hurdles we natural builders have to overcome.