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You could probably have your mail pass through a non-gmail server like http://www.mailgun.com/ first

My solution. Gmail Filter -> Forward to Mandrill Email Address -> Mandrill Webhook -> POST to HTTP endpoint that will issue a Twilio voice call to my phone.

I then have my Twilio number added as a favorite contact in iOS Phone app thus bypassing the scheduled Do Not Disturb feature. I will continue to get calls every 3 minutes until I answer the call and press 5. That's my "shit hit the fan" alarm.

you've just successfully invented PagerDuty (albeit cheaper and DIYed) ;)

http://context.io/docs/lite/users/webhooks

We currently use Gmail IMAP with IDLE to support this use case. It works great, so I hope they don't drop IMAP without a suitable replacement like webhooks.

The quotas are per user. So you can poll the /history endpoint per user. But yes, this isn't very efficient.

You could use Zapier: https://zapier.com