I use Fredrick's inside-out method.
1. I build a ledge on my walls:
![Image](https://i.imgur.com/0M382Po.jpg)
2. I glue and crown staple the ceiling in place:
![Image](https://i.imgur.com/Kw6fSzz.jpg)
3. I add my ribs. These are butt-screwed and then glued/crown stapled to the ceiling:
![Image](https://i.imgur.com/gmoh8B4.jpg)
4. The hard board insulation is glued in place:
![Image](https://i.imgur.com/WhlF6pA.jpg)
5. And the roof is glued and crown-stapled in place:
![Image](https://i.imgur.com/NujNrr4.jpg)
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