Is having no delay what everyone wants? Are the issues you discuss so time sensitive that 5 minutes is going to change something? Do people really want to have their message sent with a huge typo rather than having a minute to edit it before everyone sees it?
I think those outgoing emails get processed by a job rather than going out on real time. Perhaps it runs every five minutes? It might be possible to have that job run once a minute.
If people turn on notifications they can get best real time notifications in their browser.
Also, have you checked the email headers to see how much delay is in the mail system?