I don't know if I'm just unlucky, or if this is happening to others on Gilgamesh/elsewhere, but I recommend if you haven't already that you turn off the /tell sounds before you view the long cut-scene (the one that asks you to make sure you have time to watch it).

I have never received more RMT tells than when I've been watching the story cut-scenes for this patch; the story was riddled with the message received sound, and at that point there wasn't much I could do about it. It seems that they know they have a captive audience.

Even if SE continues to be lax on dealing with these problems, I hope this at least helps others to not have the story experience lessened by constant interruptions.