I'd be interested in a compound metric composed of the likelihood ratio and the p-value. Essentially the more likely your hypothesis, the higher your P value c

I'd be interested in a compound metric composed of the likelihood ratio and the p-value. Essentially the more likely your hypothesis, the higher your P value can be, and conversely unlikely hypotheses require stronger evidence. I don't think this solves the problem but maybe it makes that assumption about the hypothesis likelihood more specific.