Welcome to the Let's Encrypt Community, Luke 
Transferring certificates (and their private keys) for usage with certbot is not entirely straightforward. There's more to a "certbot certificate" than just a certificate and its private key. I started a topic in our lounge category a few days ago that suggests changes to certbot's behavior to address this issue that I hope to see implemented in an upcoming release. You need to be a regular, leader, moderator, or staff to see the topic at the moment, but I might open it up to the public depending upon feedback.
At present, we recommend not copying anything over and just using a clean install to acquire new certificates. This approach avoids so many problems. I could try to guide you through the painful nuances, but even making a single oversight in the process would make the effort more trouble than it's worth.
Once you have your new VPS fully functional, we can guide you through using the staging servers to ensure your setup is solid. Then we can work on getting you real certificates. This will keep you from needing to be concerned about the rate limits.