Sorry Nikodemus I can't see any reason why you would want to see the greets of people behind you, in the next room or as in the tavern upstairs
I regard /greet as a catch-all for any form of greeting, be it verbal or non-verbal. May even be OOC (in fact, I prefer to /me IC greetings), and I feel that /greet is less disruptive if used sparingly. I don't recall being particularly bothered by /greet storms, but I avoid the plaza, anyway. However, I think that a special tab, or temporary (pop-over) in the chat window would end up being more annoying than them. Also, greeting everyone if there are more than about three people to greet is a good idea, and will come naturally, since individually targetting people gets tiring fast.
Regarding the animations: to me it looked like puking, but sneezing fits even better.

I think I know what it is meant to be, maybe it's just a bit overzealous. I'll check how the swapping changes things some time, anyway.