I agree with what you said about how we introduce ourselves.
As for your possible improvement, I don't know if everyone here cares about the latter two points. But it seems that a lot do, and I'm not sure whether the amount of people are over the "threshold" where it makes sense to generalize.
Anyway, I've always felt pretty strongly that at its core, the goals of rationality are really simple and straightforward, and that it's something everyone should be interested in. At it's core, rationality is just about:
1) Getting what you want.
2) Being right.
Everyone tries to get what they want. Whether it's good grades, money, health, or altruism, everyone is trying to get what they want. And people generally don't do such a great job at it. Shouldn't they want to do a better job?
And everyone wants to be right. Everyone has their opinions on how things really work, and what will happen in the future. But shouldn't they want to be better at it?
If someone comes up to you and says, "Hey, I've got some ideas about how you could do a better job of getting what you want and understanding how the world works. Interested?". How could you not be interested in those things?!* (One problem might be credibility. Ie. people might respond by saying, "yeah, right".)
*I sense that a big problem is that "getting what you want" and "understanding how the world works" are Lost Purposes for most people. And so it's probably good to give an example of each of them that everyone could relate to, and that are actual pain points for people. Something that people are struggling with that they actually want to get better at. Not something that people should want to get better at, but don't actually want to get better at. But I think it's important to focus on principles and not sound "self-help-y" (which seems a lot easier said than done).
*I sense that another problem is that people don't want to identify as a "rationalist". I get that impression from most people I tell about the site. Other people explicitly say that it feels cult-y.
In general I don't think it makes sense to tell people about LW. It makes much more sense to link someone to an article on LW that's likely worth reading for that person. If the like what the find, maybe the read more.
I told an intelligent, well-educated friend about Less Wrong, so she googled, and got "Less Wrong is an online community for people who want to apply the discovery of biases like the conjunction fallacy, the affect heuristic, and scope insensitivity in order to fix their own thinking." and gave up immediately because she'd never heard of the biases.
While hers might not be the best possible attitude, I can't see that we win anything by driving people away with obscure language.
Possible improved introduction: "Less Wrong is a community for people who would like to think more clearly in order to improve their own and other people's lives, and to make major disasters less likely."