Have you checked out the permit/inspection exemptions the county has?
http://www.co.stevens.wa.us/landservices/documents/BuildingOrdinance.pdf section 1.4.2 has info on it.
If you have a waste disposal system then tri-county will have to approve it. If you have a simple 5 gallon
bucket composting system though (mixing kitchen scraps and human waste as
compost) then you might be able to argue there is no waste disposal system to inspect/approve.
I would get more info from the county first about what they would need to see for a code-approved structure, you might find a timber frame structure with strawbale infill works and you can go through the normal approval process instead of asking for an exemption.