What is an effective strategy for increasing rating and review volume on your preferred voice of customer channel (i.e., how do you direct customers to a specific VoC channel)?

For my company, the only strategies that worked so far are incentivized. This almost always gave the targeted channels a boost. But hard to scale over time.

In my experience, it's always been a very long process to get the response volume and quality we're looking for. 

The key was to use, either multiple channels, or the customers preferred channel to contact them and refer them to the appropriate channel we wanted the review on. 

Using multiple (or preferred) channels, we would: 
Start by giving individuals a heads up that they would be receiving a VoC survey. 
Then follow up with some additional information as to the purpose and evaluating criteria.
Then follow up when they had just received the survey (and where to go look to find it)
A reminder a few days later 
A final reminder before the close of the survey.