Are you familiar with the Mooney Wall? If not, check it out below.
Mooney WallAnother option I had considered for a modest priced moderately high R DIY wall was to build standard 2x4 @ 16" wall, then rip strips of 1/2" polyiso "
Rboard" (R3) ~2" wide on my table saw using a metal cutting abrasive blade and glue or staple those strips over the 2x4 framing. Then rip 2x4s in half and screw them over the top of the Rboard strips with a single bottom plate and single top plate for attaching sheetrock and trim. I had then planned on having wet sprayed cellulose applied to fill the cavity (cost here for material and labor is ~$1/sq ft). But you could do the netting and dense pack dry cellulose if you have access to a blower strong enough to dense pack. The advantage of this approach is that the framed wall width is exactly 5.5" wide (3.5" + 0.5" +1.5") which exactly matches 2x6 wall framing and standard door jambs for 2x6 construction will work. The Mooney wall approach is only 5.0" wide. If door jambs aren't a concern, you could further increase the R value of my approach by using 1" Rboard instead of 1/2" Rboard.