This seems like it would be fixable with a fairly small amount of money, relatively speaking: offer something like $250K for the most important papers that would otherwise be published in Nature to instead be published in an open-access journal. After all of the major papers for several months are published in open access journals and the most well-known journals are reduced to publishing only the dregs that are left, opinion could change quite quickly. Sustain this type of payment for a couple of years and I'd bet there would be a sizable number of other people publishing open-access, since to be published in Nature would imply that your paper wan't important enough to be offered the $250K reward.
(Disclaimer: I used to work in this field at biomedcentral.com)