You point out a problem: There's no way to tell which organizations are making progress on AI alignment, and there is little diversity in current approaches. You turn this into the question: How do we create prizes that incentivize progress in AI alignment? You're missing a step or two here.
I'd say the logic goes the opposite direction: because there are no clear objectively measurable targets that will improve AI safety, prizes are probably a bad idea for increasing the diversity and effectiveness of AI safety research.
Edit: In case it's not obvious, I have done limited research on AI alignment organizations and the goal of my post is to ask questions from the point of view of someone who wants to contribute and is unsure how. Read down to the comments for some great info on the topic.
I was introduced to the topic of AI alignment when I joined this very forum in 2014. Two years and one "Superintelligence" later, I decided that I should donate some money to the effort. I knew about MIRI, and I looked forward to reading some research comparing their work to the other organizations working in this space. The only problem is... there really aren't any.
MIRI recently announced a new research agenda focused on "agent foundations". Yet even the Open Philanthropy Project, made up of people who at least share MIRI's broad worldview, can't decide whether that research direction is promising or useless. The Berkeley Center for Human-Compatible AI doesn't seem to have a specific research agenda beyond Stuart Russell. The AI100 Center at Stanford is just kicking off. That's it.
I think that there are two problems here:
How to evaluate progress in AI alignment?
Any answer to that question, even if not perfectly comprehensive or objective, will enable two things. First of all, it will allow us to direct money (and the best people) to the existing organizations where they'll make the most progress.
More importantly, it will enable us to open up the problem of AI alignment to the world and crowdsource it.
For example, the XPrize Foundation is a remarkable organization that creates competitions around achieving goals beneficial to humanity, from lunar rovers to ecological monitoring. The prizes have two huge benefits over direct investment in solving an issue: