Hi robs1,
Good on you for getting this sorted before your email drops off. Saves a lot of hassle down the track. To update your login, just sign in to my.MYOB and head to the My Account menu at the top of the screen. From there, choose Change Login and pop in your new email address. Since your 2FA is tied to your phone number, that part will stay the same. You can also keep using the same password if you like. As for access permissions, you don't need to tweak anything if you're just updating your own login. But if you don't see the Change Login option, it just means someone with administrator access will need to jump in and create a new user for you with the new email. An invite will the be sent straight to your new inbox to get you set up.
Here's a handy link that steps you through the process: Change login email address.
Regards,
Sai