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I would like to use Dokku and not have to worry about the underlying software maintenance. Are there any companies offering Dokku as PaaS?

...Heroku?

digitalocean.com also has a "marketplace" of many preconfigured droplets (VPS), including "Dokku 0.12.13 on 18.04)

NodeChef does not use Dokku under the hood but you can achieve what you want and more with the platform. https://www.nodechef.com/