Seriously, how much of a single, unified purpose does Less Wrong actually serve? I'm not sure exactly of how these two goals complement each other, or how this forum's contribution to either or both is measured.

Eliezer has written a couple of posts mentioning how LW helps the SIAI's mission. As for the other way around, donating to the SIAI has been framed in terms of maximizing marginal expected utility before, which would make it an application of instrumental rationality.