Its kinda like that but its not really current limiting. Think of the Sage as a voltmeter. It is connected right across the chime input power..........hmmm good you said that...
Thinking more about the Sage input. You might have to put a small resistor across the Sage inputs. Would think a small 1k to 5k resistor. My thought is, originally the chime input insures the Sage inputs are at 0V when the doorbell button is not pushed.
Now when the button is not pushed, the Sage inputs see an OPEN circuit which it may or may not sense correctly or immediately.
I would start with a 10K resistor.
