You can’t re-add it as an other account with imap and smtp server credentials - you need to add it as a Google account.
As for the inability to add alias addresses, Dan Moren published a workaround for this, so long as you have another imap account on the phone. For example, if one of the alias addresses is an imap account, you could add that account and turn off notifications for that account, set the fetch interval to manual, etc.