Best practices for keeping a campus computer network from getting brought down by inappropriate use?
I see this as a resource allocation problem, not an academic freedom problem. Your network just does not have the resources to support many users with high-bandwidth demand (whether the demand is academic in nature or not), and your school does not want to apportion more money to upgrade network resources.

It sounds like you don't really want to prevent a particular use of the network; if you did, it would be in your Acceptable Use Policy. You just want to prevent a user from hogging network capacity, which degrades the experience for everyone else.

Instituting bandwidth caps (or a similar content-agnostic strategy) to prevent excessive resource use by one individual does not violate academic freedom. For example, Amtrak limits use of WiFi on its trains; streaming music, streaming video, and downloading large files are disabled. This is understood to be a reflection of their unwillingness to spend the money that would be required to support high-bandwidth content, not censorship.

If you want to make sure that students still have access to I Love Lucy and other essential academic content, you can offer uncapped network access in specific areas (e.g., in the library). 

Of course, if you plan to implement this, you should announce the change, explain the reason for it, and expect students to be very, very unhappy about it. "Network" is simply one of the resources that students expect from a college; from their point of view, you are failing as a college if you do not provide a reasonable amount of this resource.