I'm restoring a small barn (10' wide x 16' deep, with a 4' x 8' side
lean-to). It's built over a hillside, and supported by steel columns
placed in concrete footings, which replaced the old wood pilings. The
entire frame is 2" x 4" construction, including the rafters.

Here's the problem: I live in NY State, and need to insulate the barn
well in order to use it in Winter, as a home office. The building code
calls for R38 in the ceiling, and a minimum of R11 for the exterior
walls.

The walls are no problem, since I can install an R15 batt insulation,
and although I'd like a higher R value, I can't get it unless I build
out the studs to 2' x 6".

The problem is that the 2' x 4' rafters aren't deep enough for adequate
insulation. So here are my choices, and I need some advice from someone
knowedgable.

Forgot to mention that I'm replacing the roof.

1. Replace the 2" x 4" rafters with at least 2' x 8", or even 2" x 12"
rafters, and put the highest R value batt insulation available,

or,

2. Leave the existing rafters, and use 2 layers of rigid foam
insulation over the new plywood roof sheating. I saw some R12 rigid
foam insulation at Home Depot, so 2 layers of that (R24) and batt
insulation (R 15, gives me R39.

What's the best (and least expensive) solution? Thanks!