Do you have a floating IP address set up at DigitalOcean?
Assign a floating IP
A floating IP is a static IP address that points to one of your Droplets. It allows you to redirect network traffic to any of your Droplets in the same datacenter. For instance, if your primary Droplet goes offline, you can point your floating IP to a backup Droplet.
When your domain name points to the floating IP, then it becomes much easier to shift traffic from one instance to another as there is no wait for DNS info to propagate.