You could prompt the user through multiple pages of "questioning" under a similar premise of psychological analysis, or some other manipulation. This would reduce the number of buttons per page.

That's what I think he meant.

Not necessarily. What if the un-visited box was set to display:none? That would leave you with just the visited boxes showing.

Now make it even less obvious: create a false box with the proper :visited color. That's your bottom layer, your fallthrough if the user hasn't visited any of them. Now position all of the :visited boxes as exactly the same size and position over that bottom layer. Now, when the user clicks the button to continue, they're guaranteed to click either your fallthrough ("user has none of my sites") or one of those you are monitoring for.

The end result of all this is a page that says "Click the box to continue."