The OP seems to assume that the big danger with AI is that it will leave the people at the mercy of an (human) elite that controls an AI or that has programmed an autonomous AI (an AI not controlled by any humans) to care mostly or only about the elite.

In contrast, what organizations like the Machine Intelligence Research Institute and the Future of Humanity Institute (MIRI and FHI) consider the main danger (and have considered the main danger for over 11 years) is that the AI will not care about any person at all.

For the AI to do an adequate job of protecting human welfare it needs to understand human morality, human values and human preferences -- and to be programmed correctly to care about those things. Designing an AI that can do that is probably significantly more difficult than designing an AI that is so intelligent that the human race cannot stop it or shut it down (although everyone grants that designing an AI that cannot be stopped or shut down by, e.g., the US military is in itself a difficult task).

The big danger in other words seems to come not from a research group using AI research to try to take over the world or to gain a persistent advantage over other people, but rather from a research group that means well or at least has no intention to be reckless or to destroy the human race, but ends up doing so by having an insufficient appreciation of the technical and scientific challenges around protecting human welfare, then building an AI that is so smart that it cannot be stopped by humans (including the humans in the other AI research groups).

I fail to see how changing the AI-research landscape so that more of the results of AI research will be published helps against that danger. If one team has 100% of the knowledge and other resources that it needs to build a smarter-than-human AI (and has the will to build it) and all the other teams have 99.9% of the necessary knowledge, there might not be enough time to stop the first team or (more critically IMHO) to stop the AI created by the first team. In particular, if the first AI is able to build (e.g., write the source code for) its own successor -- a process that has been called recursive self-improvement -- it might rapidly become smart enough to stop any other smarter-than-human AI from being built (e.g., by killing all the humans).

Rather than funding a non-profit that will give away its research output to all research groups, a better strategy is to give the funds to MIRI who for over 11 years have been exhibiting in their writings an vivid appreciation for the difficulty of creating smarter-than-human AI that will actually care about the humans rather than simply killing them because they might interfere with the AI's goal or because the habitat and the resources of the humans can be repurposed by the AI.

Any effective AI -- or any AI at all really -- will have some goal (or some set or system of goals, which for brevity I will refer to as "the goal") which may or may not be the goal that the builders of the AI tried to give it. In other words, everything worthy of the name "mind", "intelligence" or "intelligent agent" has some goal -- by definition. If the AI is powerful enough -- in other words, if the AI is efficient enough at optimizing the world to conform to the AI's goal -- then all humans will die -- at least for the vast majority of possible goals one could put into a sufficiently powerful optimizing process (i.e., into an sufficiently powerful AI). Only a very few, relatively complicated goals do not have the unfortunate property that all the humans die if the goal is pursued efficiently enough -- and learning how to define such goals and to ensure that they are integrated correctly into the AI is probably the most difficult part of getting smarter-than-human AI right.

That used to be called Friendliness problem and is currently usually called the AI goal alignment problem. The best strategy on publication is probably to publish freely any knowledge about the AI goal alignment problem, while keeping unpublished most other knowledge useful for creating a smart-than-human AI.

I will patiently reply to all emails on this topic. (Address in my profile.) I do not get a salary from FHI or MIRI and donating to FHI or MIRI does not benefit me in any way except by decreasing the probability that my descendants will be killed by an AI.