Multiple chat tabs (Splittable chat window)
I think that tabs for different chats is workign well. Perhaps just having a brighter and more attention grabbing graphic for the tabs which have missed chats in them. Split your WvW/team chats into one, Guild into another, main for PVE into another. Allow whispers on all of them. Switch to your WvW one when your in there, and check guild chat whenever you have downtime/death in WvW.
I throw in my vote for allowing us to make a separate chat window that is NOT just another tab if that’s what you’re asking
Funnily enough that is exactly my current methodology for chat layout, but as an ex Eve online player, I have been spoiled by all the bells and whistles of a very customisable UI (guild wars 1 eventually had this to some extent, hence the reason I am suggesting it).
Your solution is ideal for those of us who struggle to keep up with all the goings on in various chats given the current implementation, but I hope that in the future A-Net will consider adding flexibility to the way chat can be displayed for those of us that want the option.
I would like to be able to move the chat tabs around my screen wherever I want. In most games I have the main few tabs in the default spot and a separate tab moved elsewhere on screen (usually above the main window) for guild/party/whisper.