NLF airfoil with low pitching moment

I have been searching the web for such airfoil, and it seems like there is no such thing in the public domain. At least I have not found one.

For a canard/tandem configured aircraft, the main wing should have very low pitching moment, preferably zero if possible. The flying wing airfoils generally don't have very extensive laminar flow and they are not that interesting except for some exceptions (found one Wortmann airfoil which has quite high L/D but does not really compare to the drag coefficient of the NLF414F at high reynolds number).

So what I would be looking for would be:
- a thick (16-20%) low reynolds number natural laminar airfoil which has low or zero pitching moment, has design cruise Cl of 0.1-0.2 and which would have comparable drag charasteristics than the NLF414F or not very much higher drag than the NLF414F and which would have design cruise reynolds number around 5 million (not 10 million like the 414F) and which would achieve unflapped Cl of 1.2...1.3 at reynolds number 0.8 million.

So am I looking for an impossible airfoil? If you know that someone has designed and tested in wind tunnel this kind of airfoil, please let me know!