Make sure you guys listen to this with headphones on. Couldn't hear what sounds like the cam chain rattling through laptop or smartphone speaker.
You could try that 5th/6th gear trick. Personally, I would take the CCT out. Reset it to zero(loosen the middle bolt until it allows you to bottom the shaft against it's base). Reinstall it (leaving the middle bolt loose still). Then tighten down the middle bolt. It's what I did on my 93 zx7. The automatic CCT is no different in design between these two bikes.
OR
You could just replace the automatic CCT with a manual CCT from a company like APE. You'll need to add checking/adjusting the CCT into your regular maintenance whenever servicing your bike. But, you wouldn't have the unexpected annoyance of having to manually adjust an automatic CCT when it doesn't automatically adjust. Oh, the irony.