This brings up an area that’s been on the edge of my curiosity for years: how do you combine the knowledge of the experts (contestants) with logic to do better either than either strategy individually?

It’s mostly about how to elicit the information from the contestants. Once you have the probabilities from them, it seems relatively straightforward.

I think you could do some form of Bayesian analysis with the prior being how likely each contestant thought that their available partners were "The One" for each other. Then the truth booth would be used to update your priors.