Cliff:
All rods have the relief (what I called the "step in"), regardless whether they have the barrel.
By measurement: Barreled rods 5.3mm across the relief, non-barrelled 5.0 across the relief, so the existing rods are better suited to my 12's problem, even though they don't answer it.
You are right on the threaded portion of the standard lug’s being longer (15mm above the lug body) than the ones on my 12 (10mm above the lug body).
I had not noticed that, but clearly the longer lug inserts would have allowed the tunesafe to clear the H bar, but that would have pushed the the insert and tunesafe almost up to the hoop. As the distance between the top of the insert and the hoop diminishes, the angle of offset between the placement of the insert and the hole in the rim (relative to the center of the drum) becomes effectively greater, and that angle seems to be what is pulling the lugs out of true. Thus, using the longer lug would, at the very least, make my offset problems greater even if it solved the problem of the H bar, a problem that is pretty low on my totem pole.
However, the offset leads to the question: how are these lugs designed to allow a certain amount of flexibility in offset, both to account for eccentricity of head mounting and/or to avoid cross threading?
I pulled the tunesafe cap off one of my 12” lugs, grabbed the threaded insert and tried to wiggle. Nothing. Even so, the hole through which it emerges from the lug body is wide enough to allow for some wiggle room, and the insert is pressed against the outside of that hole. That seems wrong. Repeating the same experiment with a lug on the 13, I was able to get considerable motion from the insert in all directions.
So clearly the insert is meant to have flexibility to account for the offset. Next step is to pull the 12 back apart to try to understand why at least some of the inserts are rigidly fixed. There is hope.