I finally decided to bite the bullet and have a go at converting all of my old .mdi files ("printed" when the Microsoft Office suite included the .mdi virtual printer, before it was deprecated). Microsoft kindly supplies a command line utility to help out called MDI to TIFF Converter, which--as the name suggests--converts .mdi files to .tif files.
The tool only has a command line interface but the arguments it accepts are simple. The tool will also recurse through a directory hierarchy.
I did have trouble with one document and the tool just bombed while running but it was simply enough to track down the offending file and start afresh after deleting it (deletion was appropriate in my case).
You can download MDI to TIFF Converter here: http://www.microsoft.com/en-au/download/details.aspx?id=30328