Unusual scheduling requirement

I have and unusual requirement for a sprinkler controller and I’m hoping someone here can let me know if the Rachio controller will meet my needs.

Water for my lawn is supplied from a local irrigation district. The water is delivered via a canal system. My specified time to receive water is 12 mid-night to 6 am each Saturday night during the irrigation season. However, there are many factors that can affect the delivery of the water. Water is usually available during my time slot, but no always. In addition, it is normally the case that some amount of water will get delivered to my property sporadically on Friday nights and during the day on Saturday. When water is delivered it flows into a cistern and I have a pump that then delivers the water to the sprinkler system. Power to the pump goes through a float switch so regardless of what the controller is set to, water is only delivered when the float switch indicates that water is in the cistern.

What I would like is a controller that allows me to set a duration for each zone, say 60 minutes. However, during the day on Saturday I might have water available for 15 minutes and then no water for the next 90 minutes. Then water again for 60 minutes. The controller needs to know that, in this example, zone 1 received 15 minutes of water and was then delayed. When the 2nd wave of water arrived for 60 minutes the controller needs to know to run zone 1 for an additional 45 minutes (for a total of 60 minutes) and then switch to zone 2.

An alternative might be a controller that regulates water by volume, not time. This would require a flow meter.

Does such a controller exist?

Thanks in advance for any and all advice.