What's great about my proposed challenge is that you can define "feeling better and "less tired" or "less fatigued" any way you want!
Just pick which of the two tanks is more beneficial in regard to those factors, however you care to define them and report back.
I can't run the test on myself, because I know there's no difference. I can tell you in advance the results will be 50/50.
You cannot disprove a negative, you might as well tell me to go find proof of no Santa Claus.
Finally, it probably doesn't matter why Nitrox makes divers feel better, it's just a way of helping to settle the debate as to whether there's a real physiological factor or if it's all just psychological. Nothing more.
My thought on a modification would be to have the third/outside person change the mix for the entire day. All bottles have the same gas mixture. Record the feeling at end of day (scale of 1 to 10). Then after 10 dive days, compare felt results against the mixtures of gas? If there is a benefit, mixing gases in a single day might dilute the affect?
Not saying that there is or is not a benefit. But I do like trying to get to the essence of the test.