Hey Matthew,
If you have still same problem, check out this page, it might help you:
MySql Rename
I guess you will lose a lot of time renaming all tables.
You can actually do something like this, it will save your time:
Go to phpMyAdmin to access your database.
Go to export, leave all default values and press Start. Exporting the database can take a while.
When done, select all code and copy it to notepad (or any other text editor)
In phpMyAdmin, select all tables and delete them
In notepad, do a Search & replace (Ctrl + H). Set the searchterm to 'old_prefix' and change it into your new prefix (Example: jos_). Press "Replace all".
Select everything in your notepad file and copy it. In phpMyAdmin, go to SQL, paste the queries and press Start.
Source:
joomlatools
Cheers, Petar