How do a Migrate a Sub-folder multisite install on one host to another host

We have two multisite installs: Production and Staging. We need to replicate stage to production. Each site is using a different hostname. The multisite is configured to use sub-folders, not sub domains. We are doing this because of a policy in place that states “thou shalt not work on production.” So all work is done in and tested on staging before being pushed to prod. We’d also need to auto-push from stage to live each night.

We’re playing with the sunrise.php config, but having little luck with it.

If you guys think you can help do let me know. Thanks.