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I eventually solved my own problem. Chatted with a support rep for a while. We confirmed all the things as far as connection and setup. Unfortunately, I was not comfortable enough with messing with the wiring at the valves, so I couldn’t verify voltage at the valve connections.
After ending our support chat I was fed up enough to start digging into the wiring of the valves and the master valve. I discovered that the previous owner of this house did not connect the white wire to anything. It was just sitting in the box coming out of the wall. I followed each wore and mentally mapped out where everything was going, and discovered the green wire is used as common. Once I connected the green wore to the common in the controller everything started working as expected.
The surprising part of all this is that the previous Skydrop controller did not require a common connection to operate normally. Neither the white or green wore was connected on that thing. Go figure…