If Apple "pushes an iCloud address onto you" that you don't want, why not just freaking ignore it completely? Don't share it with friends, they won't know about it. Don't ever log into it. Ignore it.

Who cares?

FWIW I use my free iCloud email account with my custom domain since Apple (unlike Google) offers that as a free service. However, I just forward all email to my GMail address and use a custom reply-to in GMail so it _seems_ like I'm using the custom domain in both directions.