Benoire:
Another option is to remove the shingles, seal the roof if not already and then add insulation boards designed for flat roofs and then reapply new shingles. I've got a SheShed 9m2 cabin that has roof insulation on the exterior side of the 20mm roof timber and its fine in summer and winter with a little heat or fan.
thats actually fantastically high performance housing style. i like that a lot. if it was air sealed and all continuous then it would be a "perfect wall" (look up what that means).
external insulation. then strapping screwed through the insulation so you can then fix the roofing (or siding). i would put a metal roof on. its actually cheaper and easier because you would have to put ply down to have something to put the shingles onto. metal roofing just put down the underlay then screw direct to the strapping.