I went to expireddomains.net and searched for ones ending in "__mail.net". Found a good, short domain that was once a regional ISP and email provider 15-20 years ago. (I still get spam for some of their old subscribers.).
I do not use subdomains for this one. Generally, I combine a simple name with a number for the mailbox name. Like "johnathan2715@zzzmail.net" if I think it needs to look like a real name, or some other word like "giraffe1238" or something like that.
It's working great.