I appreciate your thorough post. I attempted replicating the issue on my end with my email address to see if there is an issue with Android phones; the email account got added successfully.
You mentioned the other email account is working; did you change the password for this account as well? Did you use the app password?
Sometimes when you are trying multiple times to sign in, your account may get locked. Are you using the stock email client of Moto X?
Are you able to login to the webmail at webmail.rogers.com? If yes, you can close the email clients running on all the other devices, delete the email account from Moto X and add back the email account.