The domain signing with DKIM still doesn't get you a valid IP reputation. It may help to gradually build one if it's the same IP over and over, but it's still a brand new IP suddenly sending mail from $domain. If it weren't an amazon IP it'd certainly get refused or at least marked as spam and hidden after acceptance.

Just another example of one set of rules for human people and another for corporate people. Either pledge yourself to a corporate feudal lord (amazon here) or suffer.