Can't set up iCloud mail on Android 4.2.2 phone

I have a new unlocked Samsung Galaxy Ace 4 specifically for traveling to other countries with, and I have tried just about everything I can think of and every combination of server settings, and can't get past the first stage of setting up my iCloud email to work on this device. I was able to successfully add two other accounts (my own domain IMAP and another internet provider POP). Only the iCloud account won't set up due to "authentication failed".

I have tried the stock/ default Android mail client as well as a third party client, Aqua Mail. Neither can connect to the iCloud servers. I even tried changing my iCloud password, which was a pain, because you are not allowed to change it back to what it was before. I have tried all settings for SSL / TLS (when I select TLS, I get "No response from Server") , all combinations of my user name (with and without .mac and .me), both using and not using IMAP prefixes. This is all on the initial stage of just setting up incoming email, so I can't even get to setting up outgoing.

I have searched and tried a lot with no solution. Hoping someone can help here. Thanks