I got this to work just fine, using IMAP and my username @icloud with email address @customdomain. However, I have 2 custom domains, and in my case I can add the IMAP twice, which then leads to double everything. Furthermore, the first IMAP I added worked perfectly, in terms of showing my email address, but my "full name" is my email address and I can't seem to edit it. The second email address I added is annoying in that it actually works fine, but in Outlook it shows up as my iCloud address despite setting it up exactly as I did with the first account. Again, shows up as @icloud.com when composing, but the email received is the custom domain address.
I tried to get smart by adding both addresses separated by commas (like Apple Mail does) but that didn't do it either. I don't really want to mess with double everything either, so not sure I'll use Outlook until Microsoft somehow makes Outlook work better with iCloud+ custom domains.