Posting an update on this for anyone else in a growing org using Slack: Our team chatted today and decided to keep using Slack because it's awesome for remote teams and our needs. It works well for us. What we are doing now though is to us the 'Snooze' function which lets you set it on a timer. Then when someone msgs you they are told that you're in snooze mode and given the option to 'break through' the snooze and alert you anyway. We've agreed we'll only do that if it's urgent.

I think this will work well and probably scale well too.