I'm sure this observation has been made plenty of times before: a principal can gain negotiating power by delegating negotiations to an agent, and restricting that agent's ability to negotiate.

Well that sure can't be an equilibrium of a completed timeless decision theory with reflective consistency.

You're right which means that the answer to the question:

And why would the other agent react any differently to the delegate than to the source-code change or the decision in the moment?

... is "People are crazy; the world is mad."

The mistake is to conclude that vulnerability to (or dependence on) this kind of tactic must be part of decision theory rather than just something that is effective for most humans.