My simple thought is to use metal roofing and pack the shavings fully between the ceiling and roofing.
Insulation works because the unconnected cells of air. I doubt compacted shavings will work at all.
Have you investigated the R value for what you propose?
I did a quick google search and found this ;
"Packed wood shavings have an estimated R-value of roughly 2.0 to 2.2 per inch of thickness when dry.
Insulation Performance and Risks
Using wood shavings as a building insulation material is rarely done today.
While dry shavings trap air effectively, they carry several major drawbacks
:Low thermal efficiency
: An R-value near 2 per inch falls well below modern standards like fiberglass (3.5–3.8 per inch) or spray foam.
Settling
: Shavings compress and shift over time, which leaves gaps at the tops of walls or ceilings.Moisture absorption
: They absorb water easily, leading to mold, rot, and a total loss of insulating value.
Fire hazard: Loose or packed wood shavings are highly flammable and create a severe fire risk.
Pests: Organic materials can attract rodents, termites, and insects unless heavily treated with additives like borax or lime."
VAPOUR BARRIERS
The use of vapour barriers is becoming better understood and I doubt the are any natural versions available.