You could try 2x4@24" O.C. on the vertical with a 2x2@16" O.C inside run horizontally with 2" rigid SM foam on the exterior. If you spray foam the 2x4 walls, you'll have approximately an R-35, except at the timbers. But, by spanning the rigid foam on the exterior, to incorporate the infill into the the exterior shell, I don't see anyway that your house wouldn't perform as a 'super-home' based on it's thermal efficiency. Don't forget to tape the rigid foam with sheathing tape and to save money, google tiger foam for DIY application. Do price it out locally first, at least for comparison. To insulate between the posts and the sticks, use friction fit insulation and backer rod to stop convection drafts. Also leave about 1-2" of space between the post and the rigid foam so that movement of that post doesn't buckle your exterior finish.
Hope this gives you some more idea's for your home. Thanks for the tip on the pitch!