Have you tried using the Alexa App and routine route as mentioned above?
I've been playing with two solutions and both seem to work:
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The IFTTT approach with the unofficial Ring Integration (I now only use this for automating setting and disabling my Ring Alarm): [Release] Ring Integration
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Creating a Virtual Switch, then having a routine in the Alexa app trigger that switch when there is a Ring. I'm using @ogiewon's Switch/Motion driver. This is what I have stuck with.