Hey Steve,
This, to me, looks like a perfect place to take advantage of the flexiblity provided by containers. If you are currently using a container, I'd suggest navigating to that container on the file system (e.g. Portals/0/Containers/) and making a copy of that folder in the same place, giving it a new name. This will be the new container that you'll use for the Report modules that you'd like to style.
The next step will be modifying the new container itself to provide some context for styling - basically just wrapping the container in a div and giving it a good css class name - or changing the css class name if one is already there. Essentially you'll just want to make sure your new css selector is A) unique to this situation and B) wraps the entire contents of the container.
From there, you'd want to provide the appropriate css style definitions in the corresponding container.css file.
After you've done that, just go to each of the modules you have in mind and change their container to the new container that you've created.
While there are certainly several ways you could tackle this issue - I think this is a pretty quick, easy, and sustainable way to get it done.
Hope that helps!
Ian