I am currently collecting informations about how and why people do staging in the web development industry. Would you be so kind as to answer (and share!) that 2 min survey?
http://stage1.io/survey?ref=hn0
I'll be happy to discuss that in the comments too.
With regards to setting up a company to do this, I'm not sure. A staging environment really needs to be as close as possible to production. Perhaps docker will become enough of a standard that it'll be easy to match production apps much easier in different clouds...