A close relative of this question on Stack Overflow:
When you have a web site in your DMZ that needs to access production data stored on an internal DB, what strategies do you recommend using to lower the risks that come from accessing live data?
Is it even considered acceptable to have a connection initiated from the DMZ come inside of your network?
An extra detail about the nature of the site that kind of throws a monkey wrench into the machinery is that people using the web site will be competing for "spots" on a first-come, first-serve basis with others using the internal software. Because of this, as close to zero lag time between the two applications as possible is ideal.