Well, if you can read this it means that I have succesfully restored the WordPress Blog files + database on the new server. For $2 more a month, I now have 100GB bandwidth (as opposed to 15GB) and 10MySQL DBs (as opposed to 1). FTP transfer speeds are also way up.
So all in all good news! With 100GB of transfer to spare it will also mean that I will have room to experiment with other bandwidth-consuming projects.
EDIT: Well there appears to be a few glitches. “www.maelys.bio” still resolves to the old server, whilst “maelys.bio” resolves to the new one.