you could try building out from the existing walls with tar paper/vapour barrier , foam insulation and chipboard or plywood or strapping and wood siding
As far as interior sheetrock you would likely want to cut it in between the interior framing, unless you want to tear off the existing siding?
This method takes away some of your overhang at the eaves so you may also need to extend the roof a bit...
-Mark in Ontario.