Don't waste your time, you're not a magician but a cleaning contractor. Are you being paid for all this 'care'?.
The floor surface will have been 'burnt' by the uric acid from the pee splashes and whatever you do won't make that particular area look like the rest of the floor. Cleaner by looking lighter in colour certainly after you have spent time and energy on it but believe me, the next day it will just be soaked again. Even if you put a notice up asking the punters to 'shake and dance' they will drip on that spot.
In Schipol airport in Amsterdam they have these great hi-tec w.c's .... automatic taps, flushes the lot but the best thing they have is the picture of a black fly right on the bulls-eye of the urinals. That's the way to sort the problem! Psychology ;-)
Phil D