If I were in charge of the bathrooms at work, and we did not have to worry about how patrons would react, one of the following signs would be placed above the toilets:
It ain’t so neat
To piss on the seat.
If you want to get beat
Then piss on the seat.
It is possible that the latter, more menacing, statement would be more effective than the well-known “If you sprinkle when you tinkle, be a sweetie, lift the seatie.” Being sweet may not be high on many priority lists, but most people would prefer to avoid a beat-down.