I agree we don't have a perfect definition of species, but I'm wondering if we have literally any definition of race. Has anybody even tried? Is there any criteria more specific than "if two people look very different then they are different races"?

Can't say to be honest, I don't have that much interest in the topic of race beyond its informal use to define cohorts in studies. More than likely someone could start from ethnicity and expand it from there, but the whole endeavour is likely doomed from the start given the sensitivity of the subject.