Well, I think a tiered approach to testing would be best. So what you'd do is you'd get everyone to rate others based on physical looks. You would then also ask them at this point which one they would prefer as a partner.

Then, you would have audio only conversations, no names and no reference to who they were in the photos. This stage only has 2 selectors, vocal pitch and "personality". At this stage people rate both of these and label who they would prefer as a partner. EDIT: Scratch that, it'd be better to go with recorded audio message to eliminate differences in testing.

The final stage is a face to face in which they get to put everything together. Afterwards you get a preferred partner from them and interesting results should happen.

This could also be done in different orders with a variety of different selectors. I believe the final results would vary but patterns should start to emerge. Essentially, if people are choosing anything other than the person they find most physically attractive at the end of the face to face then we are proving that they're favouring something other than physical attractiveness and therefore whatever other selector they're favouring is more important than being physically attractive.

That's where I'm leaning with it anyway, someone who actually knows what they're doing and has the relevant background will be able to do a far more thorough job at creating tests than I. The question wasn't about what the test would be, rigorous tests need to be designed by someone who knows how to design rigorous tests. The question was what others don't we know factually and what would we like to know most?