You're quite right that the project file contains the definitions of the exports, along with the locations of the input reports or database, and the model being applied to it. The model file contains the template and field definitions, sorts, filters, external look-ups and summaries.
Up until Monarch 11.5, automating this on the desktop was easy - you could write a batch file with the syntax "monarch.exe project.xprj /pxall" which would call Monarch, open the project, and perform all the defined exports. More sophisticated options were available and there's a Monarch Programmers' Guide PDF which references these.
Since 11.5, desktop automation is no longer available in the normal licence. For the last three years, you could buy an additional licence (at a significant cost) which would enable desktop automation to work. In the last three months, that's changed again, and desktop automation is now available via a desktop edition of the server product "Automator".
I'm afraid that I don't have any details of pricing or system requirements, but I am sure that Datawatch sales will be able to help.
Here's a video on the Automator - http://www.datawatch.com/resource-center/webinars/intro-automator/
This was shot on an earlier version of the product but will hopefully explain things for you.