My AH often went on similar "truth crusades" trying his darndest to find out if I was cheating, proving to me that I was exhibiting all the signs, questioning where I was, how long it took, etc etc. I actually played the game along with him for a while, because I thought that *eventually* he would see that I wasn't cheating and apologize profusely. Heck, I even agreed to text him every. single. time. I took a customer to the back for a dance and every time I was done, as well as every friggin time I went to pee, went to the locker room, etc etc, and he would sit around monitoring how long every dance took and compare that with the amount of money I brought home to see if I was lying or hiding money, or if I'd spent too much time with someone which would prove that I was cheating. It was MADNESS!! At some point, I realized that AH just needed to obsess over someone that wasn't him, so he could point the finger and not have to examine his pathetic self.
Sounds like this is what your H is doing; good for you for not playing into his hands. Refuse to dance and he'll find someone or something else to obsess over or to use as justification for his woes.