Thanks for the suggestions everyone but I have finally figured it out.
Turns out to change your hosting account email address you need to change it on the forums on the
Contact Details page.
I guess it makes sense since hosting and forum accounts are linked but you'd think there's be an option in the hosting control panel too.
Suggestion for Admins: Make a page in the hosting control panel to change your email address and password, or at least put a link in the hosting control panel to the settings page on the forums.
Note: I am not talking about cPanel when I say hosting control panel.