Flat roof to pitched roof – will venting work? – GreenBuildingAdvisor

We are designing a house in Bozeman, MT – Climate Zone 6B.

Half of the house is a gable with attic truss which makes venting easy with fascia vents and continuous ridge venting.

The other half we would like to do a vaulted cathedral ceiling. Our trusses are deep enough to allow for 14″ of Loose Fill Insulation (Sheep Wool Insulation) (Well above code minimum) and maintain at least a 2 Inch Air Gap above the insulation for ventilation from Fascia to Ridge.

From what I can gather this would work except for one area above the kitchen where the pitched roof (9/12) transitions to a flat roof. My question is if we vent the soffit at the flat roof side and the ventilation gap is connected to the pitched roof ventilation gap, will the stack effect still work in this condition?

Air would enter the soffit vent, travel horizontally 6′ then up the pitch to the ridge vent. Would there be enough draw to the ridge for this to work properly?

I have been on a mission to exclude spray foam from our project so a non-vented assembly flash and batt would not be preferred.

I also don’t like the idea of doing above deck polyiso on just half of the house as the goal is to keep the two gable forms the same width and height. We are trying to keep foams, synthetics and plastics to a minimum with our build.

Any advice on how to make this cathedral ceiling (and flat roof transition) work would be greatly appreciated.