I found this on the ASPCA website:

Sometimes an elimination problem develops as a result of conflict between cats in the home. If you have multiple cats and aren’t sure which cat is soiling, speak with your veterinarian about administering fluorescein, a harmless dye, to the cat (either by injection, Fluorescite injection 10 percent, 0.3 ml subcutaneously, or orally, 0.5 mL of the same solution). The dye does not stain carpeting, but causes the urine to fluoresce blue for 24 hours under an ultraviolet light. Alternatively, cats can be confined, one at a time, to determine which cat is soiling.

Your urine dye idea is a good one! The only downside is what the vet would charge to inject it , and you would have to subject the kitties to a vet visit.