How can I backup my entire iTunes Match library to an external disk?
The solution is relatively simple. Make sure you have enough space available on your external drive (I needed about 100GB). 

Hold option (alt for Windows users) when opening iTunes and choose to create a new library. Save this library to a location on your external drive.

Turn on iTunes Match, select every song (⌘+A), right click, and choose download. Wait as your entire music collection is downloaded.

Now you can switch between your local library and offline library whenever it suits you by holding option as you start iTunes and choosing your preferred library.