The problem is that the local server will be an entirely different development installation, which will be different from a production deployment.
I recommend that you start at the “buy a new server” step, or make your “local server” be a VM with at least 2GB of RAM. You can follow Move a Discourse site to another VPS with rsync with some modifications to set up the new server with the cert from the existing server and then do local DNS changes to point to it.
OR you can just set up the test server on a new temporary test subdomain and skip the fancy DNS stuff. And if you do it this way and just have them share S3 backup config set in the yml files, then you can restore the database from the existing site to the new one directly from the s3 bucket.