Just whitelist the public IP and don't bother with authentication. Use your firewall to control access to outbound SMTP so you don't get a client relaying through your mail server.
I will also look into the IP whitelist. Are there any specific articles I can look at that?
If you've tried an 'SMTP sender' app and it worked then i'd assume it's something to do with Moneysoft Payroll Manager rather than Office365 or the Draytek - infact, i've used the exact same setup, 2920n and using a Office365 account's SMTP, for router/server/software notifications in a few locations without issue.
I'd double check the Office365 account in a email app using the SMTP settings and see if it'll send mail and similarly it might be worth setting up a dummy GoogleMail/Hotmail/Yahoo/simple mail account on web hosting/etc account and seeing if Moneysoft Payroll Manager will send mail using the dummy account.
Could I use something like thunderbird to test the smtp settings?
Ive set up a temp gmail account which works fine with the Payroll software but not sure if office365 could have an issue with the 2920n whereas the gmail account doesnt?