I finished applying a coat of paint to my shingles today.
At first, I thought that if I used texture mixed in with a blend of paints, it would cause the asphalt shingle effect but to my surprise that was not needed.
If you just use undiluted, matte paint on your birch veneer shingles, the effect is an exact match to asphalt shingles, minus the texture of course. It doesn't matter to me if they don't "feel" like asphalt because I'm just aiming for the "look" of asphalt.
I had not realized this before because I usually apply paint to my shingles in the form of a stain. The diluted paint preserves the shingles wooden look while still adding color. Direct paint really hides the wooden look of the shingles and it's difficult to tell exactly what they are made of.
With this technique you can make inexpensive birch veneer shingles have any texture you want. With a little paint blending you can create the look of stone or clay.