Even though the request in itself is pretty clear and quite easily measured, it might be worthwhile examining what the client really wants.
If time = money, the request for 'doubling time spent' could actually mean 'double my money'.
If so, perhaps the focus should shift to money instead of time. Perhaps there are other ways to monetize? Betters ads? Memberships? Premium content?
Having said that, if the client is fixated on doubling time spent - you will have a decision to make. If the client wants to penalize you somehow for not fulfilling the request, suggest you are rewarded for over-delivery. That might make them think twice - but it can also potentially make you more of a business partner than a freelancer.
Before accepting the risk, consider to which degree you actually influence user behavior. Even the best technical solution will not get attention if the content is worthless. If the client insists on you bearing the entire risk of something partially out of your hands, walking away might be the best option.