I also missed this before, how interesting Mona! I'd never have guessed you'd want to limit your neutrals, I'm very curious to hear about how this goes for you. I tried this briefly and found that it's not for me, but as a primarily neutrals gal who is rather strict about the shades I bring in, the idea remains intriguing even though I know it doesn't work for me.
FWIW, I use two sliding scales: black to white and white to brown. My neutrals include everything on the black to white scale (black, charcoal, various grays, white), then the lighter shades on the white to brown scale (cream, sand, tan, taupe, camel). I allow other browns in leathers only, and not very many of them (I do love cognac though). I also will use olive and navy here and there, but tend to treat those as colors rather than neutrals. Then I can wear any color that suits my fancy that suits me
I hope you'll post updates on this process and how it works for you!
EDIT: Meant to say that for you I would vote for cream as the second to the navy. White can be a year-round neutral (I'm slowly converting it to my primary neutral). Also black is too versatile for your coloring, I would include it as an obligatory third neutral.