Getting funding commensurate with the funding available to scientists willing to "prove" a predetermined finding will be difficult, even more so when there is not even a possibility of producing anything novel with the money. It would only make sense as an investment for entities with an interest in the success of scientific research as a whole, but the places that dole out that kind of blue-sky research money also tend to be the most sensitive about damaging the reputation of the academy currently. They'll only be interested in it once the reputation is already ruined and it makes sense as a way to rebuild that reputation.

But beyond that, anyone trying to make the academy actually earn it's position as ultimate arbiter of truth is going to get the full force of rigourous interrogation into their work that everyone else is missing out on. So to be successful they will also need to be one of the most widely read and competent investigators in their field too.