Ragnor: Why would you run it from home and failover to some form of cloud/hosting provider instead of just running it from the cloud/hosting provider in the first place?
Running from home just has too many single points of failure (power, internet, fire, theft etc).
Yes it costs money to host things properly but presumably you have a business model or plan in mind where when you have x customers it exceeds the y cost of running the servers. Most new online services run at a loss initially and require investment of time and money to build reputation and customers. Skimping on hosting will damage your reputation at some point most likely.
The whole reason Azure, S3 or even a small VPS at some hosting provider exist is to allow you to start small/cheap and scale up if you don't want to start with a high cost initial cost of owning your own servers and co-locating them.
OP already said it's because of cost - they need a bunch of CPU and RAM, which is expensive in cloud solutions like amazon. Yes lots of points of failure at home, but OP also said it fails rarely, and that's why they want to fail over to the cloud.
Everyone knows it's not an ideal setup, hosting in a data centre has many benefits, but it looks like that option's off the table.