Encoding YUV Color Space with Positive Numbers
Why don't you use YUV with a shift?

To make my example simpler, let's use the Color Space YCoCg.
So the channels Co, Cg are in the range [-0.5, 0.5].

When you encode them, make sure you encode Co', Cg' where Co' = Co + 0.5 and Cg' = cG + 0.5.