Thanks safesphere. I am familiar with the approach you mentioned. I am looking for something that I could explain to a non-specialist and I'm thinking that Lorentz transformations my be just too much for such an audience. I'm thinking Bondi's method (k-calculus) mentioned below by robphy might be worth looking into.

Charlie, Thanks for your response. I would think that it's possible to have a number of different non-equivalent metrics that "work" and so to choose the most appropriate metric one would choose the metric that most closely agrees with the way clocks and light signals behave (according to the axioms of Special Relativity). Basically, I'm looking for a sanity check.