Question: Has anyone here had any experience with running OpenBD or Railo in production? We have some legacy CF6.1 apps that need to be hosted somewhere and I'm wondering if OpenBD or Railo is stable enough for production use, won't require a great deal effort to migrate to, etc.

Answer: 
Support for cfdocument will be included in the next "major" versioned release of OpenBD.

Just to give folks a bit of background on cfdocument support in OpenBD, a commercial library was used for cfdocument in New Atlanta BlueDragon, so that had to be removed when OpenBD went open source. The "hooks" are still in the OpenBD engine, however, so it's really just a matter of implementing the underlying functionality using an open source document engine, of which there are many.
Rob, mind if I try to solve your problem by providing a different solution than your question asks?

In that you mention an interest in hosting, just keep in mind that if you mean shared hosting, then you don't need to worry about the cost of the CFML engine. That will be born by the hosting provider, and amortized over the folks on the server. As such, you will find many low- (and even no-) cost CF hosting providers running on Adobe CF (and you'll find a range of them running different versions to suit one's taste, from CF 6, 7, 8, or 9, as I write today.)

There are various lists of CF hosting providers. I offer one (and also provide pointers to still other lists) at a category of my CF411 site: <http://www.cf411.com/#cfhost>