Welcome back Ron. I kind of resurrected this thread after you had left. I only got to fish for three days over Labor Day weekend. You must be so relaxed you just melt in your chair.
In my more recent posts, I have tried to emphasize a couple of times that a light tongue weight is not the specific cause of sway. It is a reflection of an improperly loaded (or improperly balanced) trailer. That is what is critical for a newbie to understand. As I will discuss below, I don't know that "Tongue Weight" is a valid terminology or concept once a WDH is hooked up.
As I understand the general use of the term "Tongue Weight" in the manufacturers literature, it is that portion of the trailer weight that doesn't rest on the axle(s), when the trailer is level and disconnected from a vehicle. As you know, the tongue weight is a function of the position of a number of loads distributed over the trailer frame, axles, and tongue. As more weight is applied ahead of the axle, the center of gravity shifts forward and a greater percentage of the total weight is on the tongue.
When the trailer is hooked up to a TV, essentially all of that tongue weight is applied to the ball, subject to slight differences if the trailer isn't level because of sag, etc. I think we would all agree on that point. But once you hook up the WDH bars, defining tongue weight becomes difficult.
The weight on the trailer axle(s) has increased. You noted: "The down force is less than the up force due to the load transferred to the TT's axles." You have previously defined Tongue Weight as: "Tongue Weight: That portion of the TT weight which is carried on the ball coupler as opposed to that carried on the axles". Using your own definition, once the WDH is hooked up the tongue weight must decrease since the weight on the rear axle has increased.
We could go around and around debating this, and I have read over and over all of the debate here. In my opinion, once the WDH bars are hooked up, tongue weight is not a readily determined value using the standard definitions. Nor is it a particularly useful concept at that point. The loads which created the tongue weight when the trailer was disconnected are still at the same place, but because of the WDH, the trailer axle now has additional loading, and there are now new forces and geometries involved where the bars attached to the tongue.
I have difficulty when you answer your last question saying the tongue weight doesn't change based on the foregoing. I think a better answer might be something like:
NM: I’ve heard you need a certain amount of tongue weight for sway stability. Does the WD hitch change the tongue weight?
SM: Please realize that the tongue weight is a reflection of the way your trailer is loaded. Before the trailer is hooked up, the tongue should carry 12% to 15% of the total trailer weight. The WD hitch simply changes the way the total weight of TV and TT is carried by the TV and TT axles and does not change the weight distribution of your trailer.
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By the way, I don't think we should push someone to use a WDH without a caveat regarding the suitability for their particular trailer and TV. I don't use one because my owners manual specifically advises against it. I would no more disregard that statement from the manufacturer than I would ignore the tow rating of the vehicle.
