Not sure if I am reading your description correctly, but here is my first pass.
I assume that one pump has to start from the power up, so go ahead and start pump2.
First time through, pump 2 will be stopped and pump 3 will be started.
This is pretty ugly and horrible, probably should put a delay in after starting pump 2 on power up.
After the delay at the bottom of the chart, ie, as your first post states ‘when the next cycle start I want to start pump#3’.
You probably don’t have the delay, it more linked to the ‘cycle’, I just threw it in there so you could see what I mean.
Point is, each cycle, a different pump will be started and the old one will be stopped.
Lets know how close we got…