Hi tlorenz, and welcome to the forum.
Nick Osdale-Popa posted [URL="http://www.monarchforums.com/showthread.php?2663-Processing-large-volume-of-files-at-command-prompt"]a solution to a similar challenge[/URL] a couple of years ago. His post even includes a tip on how to name the output file based on the input file, as you've described as a desire to produce.
Because you'll be changing the name of the output file, personally I wouldn't even bother with a project file. Instead I'd just apply the model and use the appropriate export parameters.
You'll need to build a few loops in the batch file to process the various report types. Copy/paste/edit.