It's not a one-man shop, is it?

There ops/sysadmins shouldn't be handling customer relations/support.

It takes about 3 seconds to stand up and yell across the room to the frontline staff, telling them that servers are down and you're working on it.

Then the frontline staff should only have to make a few clicks for announcements to go out (pre-written templates outlining what's going on and what's being done to fix it) via social media, etc.