Based on the default Adjust Input Settings for this Samsung AV-R720 device, it's quite likely that it uses a custom input selection script/routine written by tech support. You could ask support to create this custom routine but it will vary from customer to customer. Once the custom routine is applied, don't touch the input setup.

Another solution is to add a clone device that would use the "InputMode" cycling command. The SmartState will track the input mode provided the input mode list is consistent regardless of the selected input function. The Adjust Input Settings for main the device would use Method 2 (discrete method) to select the input function, and the Clone device would use Method 1 (Cycling) to select the input mode. Don't forget to set the power settings of the clone device to "no power button" so that only the main device controls the power. Use the activity add feature (Yes, but I want to add more control of options and devices for this Activity) to add the clone device.