Hi @cmonty
if you send email from webmail you don't mind about SMTP authentication.
Your problem is that your public IP address (given by your ISP) is blacklisted cause maybe it's a dynamic public IP, you can avoid blacklist using the smarthost feature that enable SMTP relay through an external SMTP server, generally authenticated (or not) SMTP server provided by your ISP.
To enable smarthost feature:
1) go to Email section
2) click on Messages tab
3) click on send using smarthost checkbox
4) fill in data about SMTP server prodived by your ISP or any other else