IIUC, the point of making the agent use quining to locate itself in the world is that it allows it to cooperate with copies of itself in games such as program-equilibrium prisoner dilemma. Your proposal based on origin will fail to cooperate in such cases.

Not really. Two XDT agents with symmetric precursors will cooperate since conditioning on the output of one precursor will determine the output of the other precursor. An agent running equation (4') will cooperate with a regular UDT agent e.g. by letting pi be a UDT agent. In fact, this latter property doesn't seem to generalize to the other variants which looks like a good argument in favor of (4')!

Quining allows the agent to shortcut Gödelian logical uncertainty in certain cases: the agent can not predict its own actions before it executes them, but if it notices that certain parts of the world contain copies of itself, it can infer that, whatever function they compute, it is the same function as its own. In various cases this is sufficient to achieve coordination.

The problem is that from the precursor's point of view, such behavior is not always rational. More precisely, it is rational when there is a logical relation between the precursor's decision and the other copy (e.g. Omega copied the successor after its creation or Omega copied the precursor and used it to create a copy of the successor). It is not rational when the other copy occurs by coincidence. Indeed, a precursor running UDT will not choose to build a UDT agent in such situations.