Another two cents wrote:
So maybe you need another signal in there between "set" and the gun.
The starter calls "set," when he/she sees that everyone is set he hits a button that starts a beep, beep, beep, BEEEEP sequence. A false start is leaving before the BEEEEP, and the sprinters can time their starts from the 1st "beep."
Again, you need to read the rules as they currently exist.
Athletes are to respond to the sound of the gun, not go when they think the gun (or beep) is going to go. What you are suggesting is explicitly anticipating ("time their starts") as opposed to responding to the gun.
If you want the race to be about timing their start so they go at the beeeep, then you are removing reaction time from the equation and might as well have athletes run solo time trials with the clock starting whenever they start. As it stands right now, one component of the race is how good someone can respond to a command given at a quasi arbitrary time.