Thank you for confirming that information @Truth! My first recommendation would be to ensure your Chime Pro is being used as an extender to improve signal. To fully utilize the Chime Pro's extender abilities, take a look at this Community post on how.
The next best step from there, will be to ensure proper placement of the Chime Pro for communication from both your router and the other Ring device.
Yes it would definitely be worth trying the Chime Pro network, as it might speed up communications such as notifications. Let me know if it helps at all!