The logic they should follow is: if I am not the other, then by taking the coin flip I am doing myself a disservice by risking torture, and I gain under no circumstance and so should never take the bet; but if I am the other as well, then I lose under no circumstance so I should always take the bet.

I'm not sure what "not being the other" means here, really. There may be two underlying physical processes, but they're only giving rise to one stream of experience. From that stream's perspective, its future is split evenly between two possibilities, so accepting the bet strictly dominates. Isn't this just straightforward utility maximization?

The reason the question becomes more complicated if the minds diverge is that the concept of "self" must be examined to see how the agent weights the experiences of an extremely similar process in its utility function. It's sort of a question of which is more defining: past or future. A purely forward-looking agent says "ain't my future" and evaluates the copy's experiences as those of a stranger. A purely backward-looking agent says "shares virtually my entire past" and evaluates the copy's experiences as though they were his own. This all assumes some coherent concept of "selfishness" - clearly a purely altruistic agent would take the flip.

I wonder if I am just very obtusely reinventing the prisoner's dilemma or newcomb's paradox here, or if by making the 2 copies identical I've destroyed an important asymmetry.

The identical copies scenario is a prisoner's dilemma where you make one decision for both sides, and then get randomly assigned to a side. It's just plain crazy to defect in a degenerate prisoner's dilemma against yourself. I think this does destroy an important asymmetry - in the divergent scenario, the green-room agent knows that only his decision counts.

Speaking for my own values, I'm still thoroughly confused by the divergent scenario. I'd probably be selfish enough not to take the flip for a stranger, but I'd be genuinely unsure of what to do if it was basically "me" in the red room.