[Edit: Don't bother responding to this yet. I need to think this through.]

How do you play "cooperate iff (the opponent cooperates iff I cooperate)" in a GLT?

I'm not sure this question makes sense. Can you give an example?

Does S compute the programmer's decision using S's knowledge or only the programmer's knowledge?

S should take the programmer R's prior and memories/sensory data at the time of coding, and compute a posterior probability distribution using them (assuming it would do a better job at this than R). Then use that to compute R's expected utility for the purpose of computing the optimal GLT. This falls out of the idea that S is trying to approximate what the GLT would be if R had logical omniscience.

Is the programmer supposed to be modeling the opponent AI in sufficient resolution to guess how much the AI knows about the programmer?

No, S will do it.

Does S compute the opponent as if it were modeling only the programmer, or both the programmer and S?

I guess both, but I don't understand the significance of this question.