Why do you say funding is getting cut? NIH's budget has almost doubled in the last decade  and many of the other funders have seen similar growth as well as new funders appearing every year.
I don't think the problem is lack of funding but screwed up incentives. When medical reaseach became focused on funding the quality of the results suffered. And if the vast majority of landmark cancer research can't be reproduced much of that money was wasted.
The solution will require a huge cultural change which may be impossible. However step one is recognizing the problem. And some efforts are already underway such as journals like PLoS which publish negative results and more recently The Reproducibility Project and Reproducibility Initiative [2,3]. Still it will be difficult.
Already funded grants are getting cut ~20% across the board. There is a ton of cuts going on right now to the NIH budget, google it and take a look.
This has been happening for years now, trying to get an RO1 (large research grant) is becoming more and more difficult and it isn't helped by the constant changing in requirements.
Every other point I agree 100% with, the culture change has to happen. Nothing is impossible, and it just takes the right people to make the right things to happen. Everyone recognizes the problem, I can't tell you how many times I hear people complaining about the same problems over and over. The problem is that they aren't taking action, and with no action, nothing is going to take place. While there are many efforts in place (my project being one of them, http://omnisci.org), they need to be implemented properly.
The same rule of startups applies to science. The ideas/concept means nothing with proper execution.
While the culture change may be slow, the academic world is having a really hard time keeping up. NIH is also fighting to stay afloat. I have a few friends who work as program officers and they really have a negative outlook on the future of research funding.
You are right about the sequester cuts. I was looking at the annual numbers of the NIH front page which didn't include 2013. I wonder why 5.5% overall cuts translate to 20% cuts. The SciMag article makes it seems like they were only cutting the number of grants not the size which kinda makes sense. Perhaps they are treating funded grants worse which seems crazy. Wouldn't this potentially waste the money already spent if the project can't be finished on 20% less?
Good luck with omnisci.org this is the sort of thing that would help: open sharing of data, techniques and negative results. If this was the norm things could be very different. But one thing I have learned is it is very hard to change and organizations culture.