This actually started out as something completely different (a repeater that didn't function) but it turned out to make one of my favorite things: LOTS OF MIST!
Actually after lots of tinkering I finally managed to make a perfectly working and reliable repeater based on your design. :-)
The system design is the same as for magma-killing machine. However:
1. Each pump is powered through a separate disengageable gear (this is the important bit).
2. On the bottom of each of 4 pits there's a pressure plate, set to trigger on water 5-7.
3. Pressure plates are linked to gears powering the pumps in the following fashion (assuming the water rotates anti-clockwise):
a. NE pressure plate is connected to W pump.
b. NW pressure plate is connected to S pump.
c. SW pressure plate is connected to E pump.
d. SE pressure plate is connected to N pump.
System initialization:
1. Disengate power to the entire system.
2. Fill one of the pits.
After the pit is filled the pressure plate inside the pit triggers. As the result, the pump that will drain this pit is connected,
but the next pump in the queue is not.
Then power up the entire system. The water is immediately shuffled to the next pit
but not further because pressure plate resetting takes some time. By the time the first pressure plate resets (activating the second pump), the second plate has already triggered, thus deactivating the third pump. And the sequence goes on and on.