Why don't inverted brackets (99780) work in this SNOT 180 configuration?
The short answer is because the combined height of the two mini inverted brackets is greater than the interior space of a tile (or brick for that matter.) But you knew this already.

I realize it isn't considered standard by the rest of the world, but because the only quality calipers I had access to tonight are customary, all these values will be in inches.

An average of several measurements gives me the following values for the dimensions of several key parts:


average height of a 1x2 - 2x2 bracket............... 0.7221
average height of a 1x2 - 2x2 inverted bracket...... 0.7278
average height of a 1x2 - 1x2 bracket............... 0.4079
average height of a 1x2 - 1x2 inverted bracket...... 0.4131
average exterior width of a 2x2 tile................ 0.7239
average interior width of a 2x2 tile................ 0.6028


Now, we all know that item 1 and 2 will fit flush onto a brick evenly if a plate is added to the other side.


We also know that in practice, if you put 3 on a brick and 4 directly under that same position, the SNOT faces will adjoin where plates may be legally connected.


But here's the catch: adding the heights of 3 and 4 does not get 1. That sum does not even get 2.

It has to do with where the gap is. On items 1 and 2, the gap is under and above the SNOT part of these elements respectively. But the combination of 3 and 4 leaves the gap between those two plates. You can see this easily by attaching 4 to a brick and then laying a plate behind. You can see that the corner is square and there is no clearance like we see from hanging 1 off the side of a brick-and-plate. 

This clearance, by my measurements, is 0.07 inches. This is the height of 4 that is placed at the corner (that leaves a gap between it and 3) This corner is what makes this technique fail. This corner also explains the reason that 3 and 4 are different heights although they suit similar purposes. 

Finally, this explains why you can affix two 3 elements to the underside of a tile. Twice the sum of the height of the 3 is still less than the interior measure of the tile once horizontal tolerance is accounted for.

As a closing solution, I recommend using two 3s attached to a tile as that works in reality. But just to prove how complicated this measurement really is, LDD still thinks that your original problem is a legal connection. 

Hope this helps.