Just a quick thought: when the average new-comer looks at the chatterbox nodelet -- and once they start to figure out how it works -- it's probably pretty common for them to wonder how the two or three concurrent conversations got started, or what question is being answered.
Right now, they can find a couple links to CB history if they follow "How do I use this?" and then spot the 8th FAQ question, whose answer contains the links. How bad would it be to include those links on the page about "Other CB clients"? The history pages are a kind of "client", after all.
But the main thing is, make it easier to find the recent CB history -- unless people have "principled objections", I think it would be simple and helpful to add to the "other clients" page, so that the history could be found no matter which of the two links you take at the bottom of the CB nodelet.