That's a great looking shed Bungee,
But why is everyone fretting over the roof pitch, letting this minimum roof pitch criteria dictate the project? Is it just because that everyone is married to asphalt shingles or is it more for looks?
I made mine very low pitch ~1 ft in 20ft, 2x10 @ 16o/c ~18ft from ledger to header beam, triple 2x10 header, 6x6 posts at ~9 ft space.
Single ply rubber roof adds only ounces per sq ft, 1 seam, no leaks, not pretty but you can't see it anyway.
I needed to park truck with ladder rack under it, went as high as I could on existing structure (cottage used as shop) and my height requirement is what dictated the pitch.
Not saying go by my specs, but I've seen similar sized structures in my area built with 2x6 rafters and beams.