Installing Discourse takes ~30 minutes if that?
Just take a back-up of your site and app.yml, create a new droplet on the new OS version, re-assign the IP to your new droplet (so domain is pointing to the right, new place), install Discourse (you can quit the wizard and update app.yml, then rebuild) and import your back-up.
That whole process should take under and hour.
This process never touches your existing droplet, so if all else fails, so easy to roll back?