'"Third option is to launch a clone of the product with a different name, use it for capturing the ad traffic and then direct it towards the original product. This seems workable, but also a bit too experimental for comfort."'

You might also have the option to twist the above - similar to what I did with my product http://exmerg.com. I created a copy of it at http://gridoc.com and directed the traffic from the old product to the new one. Users gradually started going directly to the new one (gridoc) and the original web is now almost forgotten.