Control a Downstream / Secondary Controller?

Curious if anyone can come up with a creative solution. The house we bought has a 5-zone irrigation system (terrible controller we’ll be replacing with a Rachio.) One of the zones sends water to a small greenhouse.

The greenhouse is setup with its own 2-zone system (drip lines & misters) with a traditional timer controller. What the former owners did was setup the main system timer to run the “greenhouse” zone for an hour and then setup the simple timer to turn on each zone in the greenhouse for 30 mins, hopefully coinciding with the hour that the greenhouse zone is active.

My question is if there’s some clever way we can set this up to completely control things with a Rachio.