TDT does in fact sketch a fairly detailed model of “what sort of situation is ‘fair’ for the purpose of this paper”, and it explicitly excludes referring to the specific theory that the agent implements. Note that Newcomb did not set out to deliberately punish TDT (would be hard; considering Newcomb predates TDT); so your variation shouldn’t either.
TDT does in fact sketch a fairly detailed model of “what sort of situation is ‘fair’ for the purpose of this paper”, and it explicitly excludes referring to the specific theory that the agent implements. Note that Newcomb did not set out to deliberately punish TDT (would be hard; considering Newcomb predates TDT); so your variation shouldn’t either.