No worries. IJ is a fairly recent RP acquisition for me, so I totally get the non-IJ perspectives. If your crew is as odds and ends as you describe, I'm sure they'd all be pragmatic and savvy enough to determine their own best methods.
That said, gdocs work great for real-time writing -- it is super convenient for quick logs or quick writers, if you want to bang something out in the aforementioned hour or two. I am not the biggest fan of them, personally, but almost every RPer I currently know would yank out their own eyeteeth before they lost gdoc access. It's basically a Word document which you can either make public or semi-public (share the link with select parties), and from thereon in all writing is real-time. While you're writing, whomever you're logging with could conceivably go back and fix typos at the same time.
I find it difficult to compare to e-mail or threads, as it is uniquely part of this newer generation of cloud-based services. The names which get displayed in a gdoc are whatever you have attached to your e-mail account, so I suppose you could either tweak how your name displays on e-mail, or just use an RP-only address. Group convos are also doable -- a nice perk is that if you use an actual gmail account, chats get auto-logged to your e-mail account, should you want to later reference them -- and gchat is perhaps a bit more stripped-down than all the features you have in Skype chats.
I hope that info is helpful, and please don't hesitate to throw any other questions out there.