Use WP Rocket with Load Balancing

With a little customization WP Rocket can be configured to work with a load balancing setup.

A

You can configure your set up to share the cache between your servers, by specifying a custom cache folder and a custom config location:
https://docs.wp-rocket.me/article/1118-specify-a-custom-cache-folder

B

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 update_post and perform rocket_clean_post on all your servers.