I wasn't helped by the fact that the enclosure turned out to have plastic headers inside.
This reduces the available space even further as I just want to stick a breadboard onto the bottom of the box! I was able to remove these by simply crushing/pulling them off with pliers and sanding it down.
The main thing which I have learnt from this is that I need more space in my base station enclosure and I really need more breadboard space to make a neater layout. To this end I have bought a new Arduino Pro Mini (so that I can solder male headers onto it), a tiny breadboard to hold the Pro Mini and a new mini USB breakout (which will also get male headers for use directly on a breadboard) board.