"Theoretically" the relative to the full scale random noise will go down when using multiple zeners in parallel or in series in exactly the same proportion of the square root to the devices number. So if you have 2 devices output summed in parallel or in series the noise will be lower by 3dB (1.41 times). Unfortunately the LTZ1000 is rather more difficult to arrange in series if you plan to use the internal heater and temperature control, so a parallel connection makes more sense. The LM399 on the other hand, with 3 in series for ~20V, and than divided by 2, could be an interesting arrangement... .
Cheers
Alex