Unfortunately, I've decided against moving to a dedicated server just now.
After a little discussion with the rest of the team at Jambour Digital, we all decided it would be better to postpone the move for another few months.
However, by having a dedicated server setup, I realised how easily I could write a script to set up the new server, so that's exactly what I did. The script automates the whole process, to the point where it loads all of the SQL into the databases, sets up the needed applications and starts HTTPd.
To setup the new VPS, all I needed to do was run the script.
Moving away from the dedicated server is a sad moment for me, as I was so close to getting it perfect, but the fact that the connection is unreliable (due to not being a business broadband connection) I could not continue to use it.