They should make it so that people can donate to the prize of their choice to increase the size of the prize. Shouldn't we try to drive the prize $ up in order to create more of an incentive to solve each of these challenges?
So... Create capable non-profit with goal of crowd-funding important research.
Just see the Poincaré conjecture and how who solved it turned down the price
For most of the math prices the solution is a very big and inscrutable collection of mathematical theorems, lemmas, proofs, etc