Replying for the sake of ensuring accuracy, not for the sake of argumentation. Got busy, wasn't able to get back to this any sooner.

We agree on #3 actually. Disagree with the "nozzle extension" terminology on #2, for reasons that should be explained below.

Next, let me admit a significant error in my parent to your post. I wrote:

> When the velocity of the exhaust flow is > 0, even if the pressure in some section of the nozzle is below ambient, the nozzle (including the section below ambient pressure) is accelerating the flow, so every element of the nozzle's net contribution to thrust is always > 0.

The "so every element of the nozzle's net contribution to thrust is always > 0" portion of the sentence is just wrong. It is certainly possible for a segment of nozzle to be accelerating the flow and still have a net negative contribution to thrust based on the pressure component. Indeed as you correctly suggest, this is the overall mechanism by which overexpansion losses arise. Very basic error on my part.

The two roots of my disagreement with your sentence are a) the simplistic relationship stated between pressure in the nozzle vs. ambient pressure being the sole arbiter of thrust production or not, and b) the ambiguous nature of the words "produces thrust". With regard to b), I believe we agree that it is both possible to participate in thrust production and also have a net negative contribution. I prefer something like the latter phraseology so things are unambiguous. As you have proceeded to parse out the specifics of what you meant, you have also clarified your words.

Regarding point a), thinking of the nozzle in a quasi 1D sense obscures the fact that the gasdynamics are at least 2D, and flow is not just being expanded in the nozzle, in anything other than a fixed conical nozzle, it's also being turned. Let's say I design an ideal bell nozzle by a standard method such as Rao's. At the end of the nozzle, when the ambient pressure is matched to the design value, the flow has zero angularity. Now let's run that same nozzle at a higher ambient pressure, same chamber conditions. If I just cut off the nozzle to a uniform length at the point where the internal pressure at the nozzle surface matches the ambient pressure, there will be > 0 angularity. Correspondingly, the pressure is not uniform across the cut-off exit plane. It's not axiomatically the case that continuing the nozzle some finite distance along its original contour, where these loss mechanisms are mitigated even though the internal surface pressure on that segment is below ambient, will produce less thrust.

What is happening mentally is the misleading equivalence between this "cut off nozzle" and an equivalent area ratio nozzle that is designed to terminate at the same nozzle surface pressure. These are actually two different contours, which quasi 1D gasdynamic theory does not distinguish. If the flow was always uniform axially while expanding (not possible), then the simple criterion you stated (part of nozzle below ambient pressure does not make a net contribution to thrust) would be true. But while it is not necessarily way off (specifics depend on several variables), this is just too simple a criterion to be correct. This is why for the purposes of this specific discussion, I think your "nozzle extension" way of thinking about the problem is misleading and should be avoided.