My PCBs arrived at last, so I can build the final prototype, with much simpler hardware.
The main modification is in True RNG hardware - istead of external white noise generator, which also worked fine, now I use the uninitialized internal RAM state. I described that process at http://hackaday.com/2015/06/29/true-random-number-generator-for-a-true-hacker/, so I won't write about it here.
I have built six units (that much I promissed to my friends), and everything works great. Here is the first photo: