tbh, I have tried so many alternatives to this issue (as a Rails dev) and 'til today, I still find the oddest one of the all to be the only one straightforward enough to match the Heroku paradigm, that would be Hatchbox (which only dwells with Rails deployments).
I will give this a shot, but I'm skeptical. Also, I want to thank the Dokku team, since recently I tried a few deployments and while there was hiccups along the way, the platform has improved quite a lot since the last time I tried it.