Revelation! And Rage!
The negative shadows are not caused by an issue of pivot point, but the direct double pass through of faces by rays from the world light source. It has absolutely nothing to do with pivots being able to draw lines through a single face rather than two or more.
After I perfected the shadow models down to 100% accuracy based on pivots (or in my case object origin), some very few faces still have issues. If I draw a line from the negative shadow, up through nearby faces which should cause a shadow, toward the sun origin point, it passes through two faces on the same mesh.
To fix this, I need to calculate the exact angle of the sun in relation to the area, and once and for all determine if the sun is an object in a set coordinate system, or if the sun is an object with coordinate system per tile. I suspect it is per tile, because the shadows (and negatives) cast on each similar tile are, as far as I can see, exactly the same (and probably has some speed enhancing effects within the engine).
Once I can get the exact angle of the sun in areas, I can then use the sun as the checking pivot point, rather than the object origin, object pivot point, or whatever else I and many others have tried.
So ultimately, the answer was fairly simple, and possibly overlooked due to assumed mechanics. In reality, it was the angle of the sun the whole time. Now we can fix it, once and for all, and I can release a complex face checking script for exact shadow casting.
But... today I need to be out most of the day, so it won't likely get done soon.
Also, since the tile can be rotated in 4 directions, there needs to be 4 checkpoints passed before a shadow is totally validated. I have to make an assumption that the tile will be used in all 4 forms and then make sure no double pass through from the sun origin is detected. If it is, I just separate those faces to another object.
I fully suspect that the sun action is handled by a plane, rather than a point, which should make testing for the thing easy, because all I have to do is, from every face vert, test a ray up at an angle (same as the sun casts down) and see what faces it passes through. If the sun happens to be a point in worldspace, then the math will be impossible, because I cannot hope to calculate that for every tile at any distance from a 2x2 to 32x32 area. If instead the sun is a point per tilespace, it would still be difficult, but not as much so. I'm really really really hoping the sun is a plane, because then it won't matter if it is worldspace or tilespace, the plane will be the same, as will the angle.