A wave isn't a flow of synchronous text (or asynchronous posts, for that matter) - it's a standing unit of editable text + widgets + threaded comments. Sort of live-wiki-ish.
You could do the same with the logging bot if it supported line-editing command messages, then just put a GUI on top that translated the visual-editing commands to line-editing semantics. I'm not saying any IRC server/network I've ever seen does this now, but it's not out of the plausibility range and far easier, I think, than pushing an entirely new protocol. But I digress: perhaps I should just set it up myself and see if it really can be done.