Inspired by Wei_Dai's comment, and assuming that SI should have a single logical document, kept up to date, maintaining its current case:

SI could use the existing LW wiki for this purpose, rather than creating a new one

Pros:

• The LW wiki exists now; there will be no further design, development, or hosting costs.
• The LW wiki already has relevant useful content that could be linked to.
• There is at least some chance of at least some useful volunteer engagement

Cons:

• SI want the final say in what their evolving document says. It's not clear that we on LW want SI to treat "our" wiki that way.
• SI want their evolving document to contain only content that they explicitly approve. The LW wiki doesn't work that way.
• SI want their evolving document to have SI branding, not LW branding.

My conclusion: All of the "pros" are about the immediate advantages of using the LW wiki, while all the "cons" are about the longer term goals for the evolving document. That suggests we should start using the LW wiki now, and create an SI wiki later. Taken together with my last comment this suggests the following course of action: first, start putting all that unpublished work straight into the LW wiki. This is a change of the rules that require things to be elsewhere first, but I'd favour it. SI can fork the content into its own, separately branded wiki when it's sufficiently complete to do the job for which it was created.

The biggest thing I worry about here is eg an edit war where eg someone wants to include something in the "Eliezer Yudkowsky" page that SI think is silly and irrelevant criticism. If SI say "we run this wiki, we're not having that in there, go argue with Wikipedia to put it in there" then people may take that as meaning more than it does.