How to minimize foam use is 2×8 vaulted ceiling??? – GreenBuildingAdvisor

Hello! 

I’m scratching my head over the best way to insulate a roof in a renovation project.  I’m in TN (Zone 4). 

First off, I am a big time opponent of spray foam.  I am trying to figure out the best way to insulate a 2×8 vaulted ceiling while minimizing the use of spray foam.  The roof is unvented and recently re-shingled, so exterior insulation is not feasible.  As a part of this renovation, we demo’ed ~7″ of open cell foam from the roof.

My initial thoughts is to do a 2″ layer of closed cell foam to act as the vapor and air barrier, and then fill the rest of the cavity with dense pack cellulose (same as I’ll be using in the 2×6 walls).  Would this work?  Are there building science issues with that approach that I am overlooking?  Any help coming up with a foam free or low foam assembly is greatly appreciated!