@Brushwood - welcome to the community. As the Rachio was previously registered to someone else I think you may need to contact Rachio support to have them reset something in the back end. Which Rachio do you have Gen 1 or Gen 2?
Networking can be fun, you shouldn’t have to set Rachio up a a DMZ or add any port forwarding - those may cause problems down the road for the network.
What is the WiFi setup - eero, extender, etc. Also, if there is both the 2.4 and 5 GHz bands are they named differently?
How strong is the WiFi signal where the Rachio is located?
Run the RouteThis app Rachio provides and send that in if you contact their support for help and they do have some good networking help.