I've finally been able to track this down, and wanted to provide a response/set of suggestions to future users building highly complex/run-time dynamic UI's. Sorry for the length of this (and previous) posts, but I'm hoping to save others the dozens of hours of learning struggle I went through

Advice to future users having issues with conflicting depths:
--Follow ArenMook's advice and *always* use Panels to control what is on top of what.
--Never try to manually adjust sorting order via scripted calls to NGUITools BringForward/PushBack/AdjustDepth.
--Try to void using the Selection tools that bring forward/push back as well, as I've personally seen at least one case where it caused me issues.
Please note that my explanation may not be 100% perfect, as I only spent enough time backtracing code to find a fix for my situation, not to fully understand exactly what NGUI is doing when (I want to make my game, not become a PHD in NGUI-ology!).
The long and short of it is that Arenmook is right: NGUI does not, on it's own, muck with depth values, but there is a big caveat: as far as I can tell, any use of the NGUITools calls that can affect depth for any widget can/will affect many other widgets along the way. Specially, NGUITools BringForward, PushBack, and AdjustDepth all have the possibility of affecting other widget's depths, either through the calls to NormalizeXXXDepths, or directly (in the case of AdjustDepth).
In my case, I started off not being aware of the proper use of panels, so everything in my scene had the opportunity to overlap. I used old school techniques of manually drawing up a UI design (on paper) with fixed depths to control draw order (which in and of itself isn't that much of an issue), but failed to account for run time generated UI elements that were copied from prefabs, and therefore kept the depth values of the prefab.
To fix the inevitable issues with depth order conflicts, I started using NGUITools to bring forward/push back, and in some cases directly with adjust depth, but they really can't solve the issue due to how the "NGUI way" expects panels (which is good, don't get me wrong).
I realized I couldn't do it that way, so moved to using Panels,
but never took my old NGUITools manual adjustment calls out of the code. My panels solved most of my problems, but ones like I describe in previous posts here would still crop up as those NGUITools calls got hit, and somehow affecting UI Elements that appeared completely unrelated.
After completely removing every single NGUITools call related to depth, all of my UI's started working perfectly under the panel structure.
Just this morning, I used the Editor's "Bring Forward" on one small close button that I needed to move (and couldn't grab with the selection tool), so I brought it forward with the Selection menu--and broke 3 other widgets depth control in the process. Undoing the Selection/Bring Forward in the editor fixed the broken widgets, leading me to conclude I should never use those tools (and ArenMook commented above that he doesn't use them himself if I understood it correctly).