First of all, quit Mail.app if it's still running.
Open up a Terminal and use the following commands to change your Mail.app preferences file to an XML format – the default format is binary, and you can't edit this.
plutil -convert xml1 com.apple.mail.plist
Then, open this file
com.apple.mail.plist with a text editor of your choice, preferably one that highlights XML syntax, but you can also use TextEdit:
open -a "TextEdit" com.apple.mail.plist
Now, look for the key called
MailAccounts. It's value is an array, with
dict children. Here, you'll find all your mail accounts in the order they were created in.
You can now manually move these
dict children around. Save the XML file and reopen Mail. Now, your Mail account order will be changed.
To prove that this works, here's a screenshot before:
And this is after editing the file: