I've actually experienced targets that succeed and targets that completely fail.
Set a target of no more than 3.30 hours, allow for the inevitable complaints, cut the rough and stay strong. Most importantly, let your Pro Shop know that you are backing them fully in implementing this policy and make sure you have notices up, old British style in their directness. Only a strong 'no ifs, no buts' approach works.
Oh, and make a fairly generous concession for groups allowing others to play through. By doing so, rather than people always feeling that the clock is ticking and therefore they must carry on regardless, they can actually feel there's LESS pressure on them to hold the rest of the course up.