Multiple domains powered by one rails app
Heroku isn't your only option. If you can anticipate your customer's domains, have a look at this. If you can't, Rails routes constraints and a combination of the accepted answer to the question linked above should get you where you need to be going. Sounds like you wouldn't want to restart your server--so no editing of the routes. You might also make domains part of your models, or distinguish at the controller level or use URL rewriting in your web-server layer.
The problem, as I see it, is that Rails breaks its mantra of opinion over configuration here. There are many ways of serving up from multiple domains. That might be an intrinsic complexity, but the Rails Guides could at least document one possible solution.