Jeromy Anglim is a doctorate-holding psychology lecturer, and like me, has his highest rep score (for whatever that's worth) on Cross Validated. Artem's expertise bridges both computer and cognitive sciences. @what has his second highest rep score on Writers, and has some professional experience in clinical psychology if I'm not mistaken. According to their profiles, Ben Brocka has a degree in psychology but works as a programmer, Keegan Keplinger and Ofri Raviv are neuroscientists, and Alex Stone is both a programmer and sleep researcher. H.Muster and John have much higher rep scores on SO, but only Josh Gitlin states that he is a software developer and not a cognitive scientist. I don't think your perceived rule holds very well at all; most top-scoring users seem to be "exceptions" in some sense.
Personally, I found this site by exploring the long list of sites on Stack Exchange after getting involved in Cross Validated, which is about statistics, not programming. I am not much of a programmer, but I have a doctorate in social and personality psychology. This beta site isn't really new (it's over 2 years old now), but some have said it doesn't retain professionals and experts very well. I will probably stick with it myself though, and I see others with plenty of credibility popping back in once in a while.
@Artem, whether we're doing enough to sustain the site is debatable. I think we're hanging in there so long as SE doesn't get tired of waiting for us to reach "critical mass". We may not graduate anytime soon, but I don't see any indication that we're going downhill. The basic design of the site produces cumulative growth, so I hope we can at least trust that what we have accumulated here so far is generally appreciated and will be supported in its growth at whatever rate it can manage.
I agree that site promotion is a priority, but I don't think it conflicts with "fierce" moderation (nor do I find our moderation particularly fierce; are you sure you spend that much time on SO?). I'm still having a hard time recommending this site to my colleagues because, at any given moment lately, most activity seems to be from new users without a grasp of how to ask a clear, appropriate question. Promoting this site probably won't make that problem go away IMO. We will continue to have a lot of moderation work as long as the system for it remains unimproved (this reminds me, I owe meta a proposal for guidelines regarding tolerance of new users' undesirable contributions and for making the account suspension decision). If we accumulate more professional (or at least dedicated and competent) users though, they may dilute the overall level of dubious content and help shoulder the moderation workload.
Generally, I wait for contextual excuses to promote this site's content. I've linked specific pages with answers of mine when I've answered other, similar questions on ResearchGate (e.g., "Can a psychopath be cured?" there, and "Is a person with a psychopathic disorder aware of it?" here). I shared a technical question with a couple colleagues whom I thought could answer it, but that question was deleted by its author. In my experience, most recent questions are either not really worth sharing, easily answered by myself, or pertain to some topic that neither I nor anyone I know would likely be able to answer without doing some research. Challenges like these incline me to spend most of my time on creating new answer content or working on existing content (e.g., voting, editing, reviewing, etc.), not on promoting the site in general as is. I know others are working on promoting it though, and I depend on them somewhat to keep at it so I won't feel the need. I think when the site is in better shape in general, I will spend a little more time recommending it to colleagues without any particular contextual excuse though. I.e., presently I wait for some specific topic to come up and respond by linking relevant content here if I know of any; in the future, I will just initiate correspondence to recommend the site in general to my colleagues regardless of whether they are actively pursuing particular queries that we address already.
Any increase in this site's popularity probably entails some increase in the influx of pop psychology, self-help, and pseudoscientific questions, not to mention questions of other problematic genera. This is somewhat of a crisis of the science itself, not just this website. Psychology is relatively young and very broadly appealing. It pertains to a lot of very challenging, esoteric questions that are difficult (maybe even impossible in some cases) to answer scientifically, so it becomes a de facto harbor for all sorts of underdeveloped and sensitive questions and attracts a lot of frankly half-arsed answers. The challenges involved in producing strong evidence and conclusive answers are substantial, but many questions appeal to intuition in ways that make them seem deceptively easy to answer. Many people who are fooled by these appearances are also naive about the limits of their own knowledge and understanding of pertinent epistemic issues.
It takes a certain amount of experience, and maybe even some talent to recognize common limits of cognitive scientific evidence, such as those restricting causal inference and cross-cultural generalizability. These inherent challenges plague professionals and novices alike, but novices less often realize this until their attempted answers face some external test, such as the feedback of the community or our moderating actions. Even professionals often fail to realize their own errors until their manuscripts are rejected or criticized after publication. We can't expect much to change anytime soon with respect to these problems, so to some extent we have to accept and work with them.
If you have any specific criticism of present moderation practices, you should probably elaborate. I'm not sure who you think is focusing on moderation anyway, aside from the moderators I suppose. Regardless, I get the impression you're unaware of ongoing efforts to promote the site that have coexisted with moderating work for quite a while now. You may want to have a closer look around at meta-questions that share your question's tags.