My own view is 'not much', unless SI were to launch an actual 'let's write AGI now' project, in which case they should invest as heavily as anyone else would who appreciated the danger.

Many of the layers are standard computer security topics, and the more exotic layers like homomorphic encryption are being handled by academia & industry adequately (and it would be very difficult for SI to find cryptographers who could advance the state of the art); hence, SI's 'comparative advantage', as it were, currently seems to be in the most exotic areas like decision theory & utility functions. So I would agree with the OP summary:

Perhaps the folks who are actually building their own heuristic AGIs are in a better position than SI to develop safety mechanisms for them, while SI is the only organization which is really working on a formal theory on Friendliness, and so should concentrate on that. It could be better to focus SI's resources on areas in which it has a relative advantage, or which have a greater expected impact.

Although I would amend 'heuristic AGIs' to be more general than that.