The Pritchett and Sandefur paper is itself a bit of a straw man: the authors have obviously produced a rushed piece of work to try and get ahead of others doing more careful analysis. It's a weak and basically ignorable contribution so let's focus on the real issues.
In your reply you say that the debate on external validity is "same old, and by now feeling somewhat tired". Last I checked that debate hasn't actually happened. Did I miss the Mostly Harmless Econometrics section on that?
"at the extreme, any finding today is irrelevant for a project being designed for tomorrow. Soooo on and sooooo forth…". So your response is basically to yawn at the problem? What happened to 'rigor'? Or is that only for internal validity?
The basic fact is that you don't know how to rigorously obtain policy lessons. Isn't it about time you said so?