I'm currently finishing my attic and I am wondering what insulation I should use in the ceiling. I was planning on using R38 or higher in the vertical and horizontal sections but in the angled sections I don't have a lot of room. They are 2x8s and after the baffles there is only 5 1/2 inches of space. I could put R21 into that space but that doesn't seem like a lot. I'm in zone 5 and I think the minimum would be R38. I was thinking about adding a 2x4 or 2x6 to allow thicker insulation. Would this be a good route to go?
Use polyisocyanurate sheet foam insulation for that part, which is (I believe) still the best insulation value per inch available to mere mortals with budgets. If you don't have a budget, aerogel..
Sheet foam over the framing and under the drywall (with longer drywall screws) is another way to get more insulation, and block the thermal break of the framing members as well. That can be combined with batt or cellulose behind, or with more sheet foam between rafters behind.
I would build the rafters down with 2x4 or 2x6 and retain airflow against the roof with plastic or cardboard channels (baffles). You don't want to create a "hot roof". A simple way to do that would be to counterbore most of the way through the two-by lumber and use 3" construction screws.
If you get about R-40 on the top, say R-30 on the slopes with fiberglass batts, and R-19 on the walls*, you'll have a reasonably modern building envelope without the expense and hassle of rigid foam.
* They are just walls. Don't go overboard with twice the insulation the rest of your walls have. Since the slopes are halfway between walls and ceiling, they don't really need full attic insulation either.