Here's what I did to bypass the issue, basically switching from Office365 to Google Workspace for this one account :
1. Go to 123-reg.co.uk and buy a cheap domain for the school, no hosting is required. Costs about £15.
2. Sign into Google Workspace (sign up if you haven't already, it's free for education).
3. Assign the domain, and verify, updating the MX records on the reg-123.co.uk site from the information on the Google admin page.
4. In the Google admin page for the domain, create a new user with an email address ending in the new domain. You also have to give them superuser privileges - I know annoying, but for us it's the only way to get past the SSO setup we have for our school - you might not need to.
5. Under Security on the admin.google.com page, turn on "Less secure apps".
6. Sign in with the new account and turn on IMAP via the gmail settings cog. Go to the accounts page for the account, then security. Turn on "2 Step Verification", with this on, you can now create an "App Password".
7. With the app password, I head over to FMS, and enter:
Mail Server: smtp.gmail.com
Port Number: 587
Use STARTTLS: YES
REQUIRES AUTHENTICATION: YES
USERNAME:
PASSWORD:
All sorted.
Issues:
The annoying thing with all of this is it means suppliers are going to get emails from a new/different email address than the one they're used to.
I've set up a forwarding rule so any messages that do come in via the new account, automatically get forwarded to the old finance email account.