Thank you - yes I did, many times.
I finally found the winning configuration:
Server: smtp.gmail.com
Username: mygmailaddress@gmail.com
Password: *************
TLS enabled
Authentication: AUTH PLAIN
Port: 587
I had to do the Unlock Captcha after entering these settings. I had already done this, but for the benefit of anyone trying to do this in the future, remember you need to set up your personal e-mail as a "send mail as" account in Gmail settings. It does not need to be an alias. Set it as the default "send mail as" account if you want to send mail as your own domain account - not sure whether this undermined my original objective of not being blacklisted if Gmail is still sending through my personal SMTP server.
I don't know if it made a difference but I also enabled IMAP in Gmail.
Thanks for your help!