If by professional you mean specialist, then the set of all non-specialists is very large. There are certainly many professional people within that set who are out-of-field but smarter than the people within it, given the tiny size of most academic fields.

I think anonymity for reviewers and cash incentives are a great idea, but that already exists, it's a market. I don't think we need any clever or new solutions here. Simply stripping science of public funding would force it to convince large numbers of people (via markets) that the science is being done well and actually going somewhere.

It would also bring scientists within the purview of all the mechanisms that have evolved to handle fraud in the private sector, mechanisms like prosecutions, lawsuits, regulators, consumer reviews, trademarks and so on. Consider the huge difference between how Theranos was handled vs how the fraud coming from universities is handled.