Yeah, science needs to reinvent itself.
How about this: instead of going through publishers, researchers are required (by their funding organizations) to put a bounty on falsifying the result (for, say, 10 years). The higher the bounty, the higher the 'impact factor'. Put your money where your mouth is. A bounty of at least the cost of the study should be expected for serious research.
I can imagine a 'falsification insure' industry. They'd look at reputation as well as employ people close to the subject matter to asses risk, taking over the role of peer review. But with aligned incentives.
This way researchers and institutions who don't care too much about truth are marginalized; they either have low impact factors or they'll need to pay huge falsification insure fees.
And researchers who are sceptical of certain results will have an incentive (money!) to try to replicate it.
Remaining question: who is the authority on whether a publication has been falsified?