The timing difference is of order the slit separation divided by c, call it d/c. To get interference, you need the wavelength, call it l, to be of order d or larger. Since the period of the wave is l/c, this means the period must be of order or greater than the timing you are trying to resolve. You cannot resolve the timing of a coherent wave at scales of its own period. Put differently, your setup is having a little fight between the need for the wave to have a sharp frequency, so you get the interference pattern (that's why lasers are often used), and the need to have timing resolution of order the wave period. You can't get the latter with a sharp frequency, that is a basic wave property.