Thunderbird and Custom Icloud Domain

I have my own email domain and moved to icloud by changing my MX records. Things are good and mail is coming in. I also use Linux and love Thunderbird. I create the Thunderbird account using the app-generated password and it discovers the proper icloud server settings. When I click Done, I get "Unable to log in at server. Probably wrong configuration, username, or password.

Everything I read says the username is the problem. However. I have tried every way with the username to and no results. icloud gave the the password so that can't be wrong. What username should I use?

Thanks!

[Edited by Moderator]