Perhaps it would be useful to change the framing?
For example... if I join a book discussion group:
I understand that much of the discussion will not make any sense to me if I haven't read the book, and that there's a rapidly reached limit to how usefully I can participate in the discussion without having read the book.
I don't expect anyone to expend a lot of effort justifying the reading of the book to people skeptical about the benefits of doing so.
I don't expect anyone to summarize just the interesting parts of the book for me so I can participate in the discussion without actually reading the book.
All of this remains true even if the group welcomes new members who haven't read the book yet, but who hang around because the community's discussions seem interesting.
So, perhaps encouraging a similar attitude with respect to the Sequences would help manage some of the PR issues you identify surrounding them.
Of course, none of that would address the SIAI-related issues. Then again, from my perspective LW is already fairly separate from SIAI... at least, I participate in the former and not in the latter and nobody seems to mind... so I don't see a problem that needs solving there.
But I would not object to further separation, if a consensus emerged in favor of that.
ciphergoth considers LW "a fan site for the sequences" (quote from Sunday). But this is only clear from people talking about them.
I was recently thinking about the possibility that someone with a lot of influence might at some point try to damage LessWrong and the SIAI and what preemptive measures one could take to counter it.
If you believe that the SIAI does the most important work in the universe and if you believe that LessWrong serves the purpose of educating people to become more rational and subsequently understand the importance of trying to mitigate risks from AI, then you should care about public relations, you should try to communicate your honesty and well-intentioned motives as effectively as possible.
Public relations are very important because a good reputation is necessary to do the following:
An attack scenario
First one has to identify characteristics that could potentially be used to cast a damaging light on this community. Here the most obvious possibility seems to be to portray the SIAI, together with LessWrong, as a cult.
After some superficial examination an outsider might conclude the following about this community:
Most of this might sound wrong to the well-read LessWrong reader. But how would those points be received by mediocre rationalists who don't know what you know, especially if eloquently summarized by a famous and respected person?
Preemptive measures
How one might counter such conclusions:
So what do you think needs improvement and what would you do about it?