Redundancy? We have "the cloud", we don't need redundancy!
You have the right idea: go private cloud first, fail over to two different public cloud providers. Anyone one who puts their business completely in one company's cloud bets their business completely on the other company's cloud business model and priorities.
The cloud model is valid for flexible resource allocation, but don't get suckered by the hype.
Amazon's cloud is their excess
capacity after their main business demands are met. If their main eCommerce needs are high, everyone else is stuffed, IMO.