You're right that the voiced and unvoiced pair ð and θ probably belong together, as is the case with other voiced and unvoiced pairs. This would also significantly reduce the disambiguities that need to be manually resolved in Step 3. I chose to put θ into category 8 though because intuitively it sounds more like f than t to me, possibly because I'm not a native speaker. I might change my mind about it if it turns out to be more practical to have them both in category 1.

I like your idea of using the major system as a form of steganography. It would require a deterministic encoding algorithm though. I might explore this idea in another post in the future.