There are a variety of ways one could fill the cavity I suppose

around here, fiberglass is still the dominant method of insulation, and after that I would suppose dry blown cellulose

I am weary of foam, because it does not breath. In Central Indiana that is a huge huge problem, moisture will will will cling to it, it happens every time. But that's not our discussion so lets not go there!

For insulating the system, I would prefer to consult with an insulation expert that I know rather than try to figure it all out myself.

there is also the possibility that the intermediate sheathing would stop short maybe a foot or 8" or some such from the top plate, allowing the outer cavity to be filled with blown in insulation from the inside.

The method I am considering is a hybrid insulation, with cellulose blown into the outside cavity and fiberglass used in the inside cavity. large factors in this are ease of installation, and also ease of wiring, etc. in the inner cavity.

I know fiberglass doesn't have the highest r-value in the world, but I think in a hybrid system like this it could help lower the costs of the system quite a bit.

Now of course the whole story changes if you use the method that involves attaching the drywall to the timber frame before attaching the light frame to the outside. i'd have to think that through a bit...