Use WP Rocket with Load Balancing
With a little customization WP Rocket can be configured to work with a load balancing setup.
You can configure your set up to share the cache between your servers.
If that is not possible, WP Rocket has a lot of hooks and functions your developers can use to implement customized actions.
For example, there is the function rocket_clean_post() that will clear a post and all the content associated from the cache. So you could write a custom function to hook into
rocket_clean_poston all your servers.