For some people, side sleeping is the best way to reduce sleep apnea, which can be worse when sleeping on one's back.
Personal experience: I had been falling asleep on my side and waking up on my back. Back sleeping is more comfortable for me. I decided to fall asleep on my back, and it was easy. Then I was diagnosed with sleep apnea. After trying CPAP, I was told that when I'm sleeping on my side my apnea was sub-clinical. The trade-offs made side sleeping the best choice for me. It was not easy to train myself to do side sleeping.
You could keep the current legal system and use the "Keynesian beauty contest" as a way to evaluate judges for retention. Are their actual decisions likely to win the "Keynesian beauty contest"? If not, that could inform the decision whether to retain. Once the community has seen the "KBC" functioning as a useful tool, it may be easier to consider implementing something like your KBCJ system.