I use Fredrick's inside-out method.
1. I build a ledge on my walls:
2. I glue and crown staple the ceiling in place:
3. I add my ribs. These are butt-screwed and then glued/crown stapled to the ceiling:
4. The hard board insulation is glued in place:
5. And the roof is glued and crown-stapled in place:
Nearly bomb proof.
Can you cut a mortise into those walls with a router and a template? Even if you can't you could butt-screw them and then glue the ceiling on and glue and screw it to the walls.
Tony