Your grouping suggestion is good and one I've used for some time. The others make less sense for me.
If you're in the TS AFK channel, you're away by definition, or you don't want to be reached at that moment. If anyone ever complains at you that they didn't get an invite when they are sitting in AFK, I don't have a lot of sympathy for that.
Likewise with League clients. I don't view it as much of an inconvenience. I guess I'm just used to inviting people who don't respond. It happens.
Thanks for the post.