(Edit: I just looked at clicky. It's great, and looks like it has a lot of features that we'd use, but your most expensive plan isn't even close to the capacity we would need.)
There aren't many products meant for tracking a site like that, and the ones that do cost thousands per month. You are paying just $10 for chartbeat. They are probably losing a lot of money on your account just on the bandwidth consumed.
I mean in the nicest possible way, but we don't have any desire to track sites that big. The largest we allow is 500,000 daily page views, and sites that big are paying us at leat $100 per month.