The rigor depends on your alternative hypothesis. If you limit your method to methodological naturalism the testing is less rigorous as you can ignore alternatives like @Winston_Ewert proposal or having your de novo gene models deal with sequential searches.
You then can also compare your alternative of LUCA to multiple origins using random change prior to selection to produce P values. Based on this method LUCA will always be statistically more likely than multiple origins.
This is why I think for biology at this point the design detection process (Behe) is valuable because it is the only method that can land you on the possibility of multiple points of origins of living organisms.