Really? Do you run a highly reliable email service yourself then? I certainly would not use gmail if that were the case. You should seriously look at why you are so reliant on email, as it is not really a reliable service, the mail servers at the other side could easily delay mail for 6 hours, it is only a best efforts eventually consistent protocol with very long delays allowed (you don't normally get bounces for days if the mail is queued for retry).
Well the world of business tends to rely pretty heavily on mail, not sure what other methods of reliable messaging there is?
Sure there is phone calls etc, but emails are used when you need an actual record of something. Also relying on mailservers to not bounce the emails and actually deliver in the end is laughable, when mailservers do go down this hardly ever happens properly.
Well, websites (or APIs) are generally much more reliable forms of messaging, because you can get immediate feedback on processing. The OP said it was business critical; most corporate email is not business critical, and missing business critical email in a channel with spam, high volume unimportant messages, and also relying on a human to answer stuff is all pretty unreliable. Sure you can feed email into a ticketing system, but at least there there is also a web interface (so you do not rely on email).
If you need a record of something, I do not think that unsigned emails are legally binding anyway, again you should probably submit signed contracts over the web not email.
If it is not time critical, email can work, but the OP said a six hour outage would be a problem, and I still think that is one they have created themselves and is a business risk.
It sounds like email isn't critical for the corner of the universe that you operate in -- good for you.
For lots of people in different roles, email is an essential tool for getting work done. Not everyone has a role that can be readily translated into an API. Business Dev/Sales for example, depends on email to communicate with the various folks that they need to engage in. Whatever those folks do, it ends with the company getting a check, so it's important.
Generally speaking, it is pretty inexpensive to deliver a 99.9% available mailbox with a 100% guarantee of external mail delivery. The fact that Google bungles a conversion from free to paid service so poorly is a sad statement when they are supposed to be a shiny alternative to the traditional Micrsoft messaging stack.
Bus dev/sales can survive a day without email every now and again (in my experience, far more than a day without a phone system). Everything will resume the next day, sure it pays the bills but a six hour outage is not "mission critical", it wont stop the "check" from arriving (email is not a payment method after all).
I have known large (email dependent) businesses have 2 day outages on the traditional Microsoft mail stack too. There are coping strategies. It is annoying not mission critical.
Are you serious? Running my small business, I used email to communicate with my coworkers, potential hires, customers, prospects, partners, potential partners, reporters, accountants, lawyers, banks, web hosts, PayPal, UPS, various government departments etc etc. Being completely cut off from that for effectively an entire business day would be destroy my ability to get anything outside "solo hacker in basement" coding done, and there really isn't a sensible mitigation plan or alternative to e-mail for this (unless you'd like to convince my bank to start posting, say, notifications of incoming wire transfers to a web form of my own design?).
Your bank provides a website you can poll to find out about stuff. Not ideal, would be nice to have a proper API, but so far we only seem to be getting these for credit card payments but this is changing (eg see gocardless). For most of those things you list you could manage in an email outage, as you have phone numbers or other alternatives.
If it is that critical do you have 99.99%+ (52 minutes a year) uptime guarantees on your mail service? That is what you are asking for, and to actually deliver that (rather than an empty SLA promise) is something that very few businesses actually try to work to, especially small companies. Gmail certainly does not try to provide this.