The 20cLC is the best stamp to use to figure out the rare 2D paper. For years I was unable to even find this paper in my stamps because it is so thick and opaque to the transparency scan technique I had used. When I started back scanning on a black, filter-darkened background it became easier to spot these. Also, I lucked out and came across the large block of 20cLC I have shown before-that was a big break.
Here is the 2C. The design seems cloudy because the 2C paper is fluffy and makes the ink go sideways when the stamp is printed-like printing on a fluffy napkin.
and here is the 2D, notice that the background in the center is much lighter and that the design is well defined.