We have many systems to go on over the last few hundred years of science. We have the pre-war system, primarily funded by private philanthropy. We have the communist system.
None of them seem to create the stream of highly replicable studies you want.
That may indicate something deep about how people work and how science is really done, and suggest that your admirable goals are not tenable.
This is not necessarily because we're worse people than them, but because the problem is now much much harder. It's always better to acknowledge that hard problems are hard, rather than trying to solve them by pretending they're easy.
As for the model I would propose, I believe all funding models are fundamentally flawed, and the best model is all of them at once, so hopefully the flaws at least sort of cancel out. At the moment, that generally means seeking a decrease of the current government funding strategy and breaking the peer review monopolies, not because either of them are necessarily especially bad, but because they are too powerful and their flaws are coming to define the flaws of science in general.
Some of this would just be a mindset change, to recognize that "research" isn't isomorphic to "producing peer-reviewed papers" and that there's nothing wrong with setting up some equivalents of Xerox Park in other disciplines. Potentially with government money, since my point is more about multiple models than the literal funding sources. If "science" as it is practiced today was less pedestalized, this would be a much less horrifying suggestion.
As you can see from http://www.pewforum.org/2013/07/11/public-esteem-for-militar... , the military, teachers, and medical doctors are on higher pedestals than scientists.
That said, I'm all for the mixed development model.
I still maintain that the military is still on a higher pedestal than science, in terms of funding and prestige. You hear stories of people buying military people in uniform their meal, to honor their service. That's much less common for scientists.
I'm not to impressed by "well, that's not how it works right now". The whole problem is "how it works right now". That's what we're discussing, the need for it to not work that way.