Mystery solved (sort of...)

OK, here is the result of my playing with the device and the house meter.
My house  is connected to the utility through a digital smart meter. My meter looks like the picture attached to this post except that it is made by Landis & Gyr.

I do not know how old the meter is (it looks relatively new) but should've worked just fine, all considering. However, it has the same design fault as my dumb Kill-A-Watt device. Under certain conditions it does not work properly.
Yes, there is still power consumption but the meter doesn't want to know about it.

My next (and rather obvious move) was to go to a friend's house where the meter is still an old winding type. No pleasant surprises there. It shows some power consumption the moment my device is plugged in.
We also tried a different digital meter (GE, bi-directional) which worked just fine and showed true consumption.

After some digging I found this video: https://www.youtube.com/watch?v=yQdeLQqaStA which shows the tear down of a smart meter. After watching the video and some additional experimenting I think I know the answer.

So, is my device consuming power? Sadly, yes. It does.
The smart meter doesn't register the consumption because it senses the current on the hot sides only. My device, however, once tuned to the resonance frequency of the transformer, draws the power on the ground side hence bypassing the sensor.
That bypassing is possible due to yet another side effect which I am not going to discuss in details as it will lead to replications of this cheating device.

(If you are unfamiliar with the US power distribution, 2 hot sides (220V AC 60HZ)are coming down from the pole. Next the hot sides are distributed evenly to level-out the load bringing 120V AC to end consumer.)
I am not going into the details of the ferroresonance phenomenon here, as I am sure you've tried  it. If not, here is a good read:

http://www.mdpi.com/1996-1073/4/9/1301/pdf
http://www.powerqualityworld.com/2011/04/constant-voltage-ferroresonant.html

Next obvious step was to try and change the resonant frequency and see what happens. Sure enough getting away from the critical point brought back proper meter functioning. Kill-A-Watt, however, remained dumb no matter what I tried.
BTW, my playing with resonant frequencies resulted to two additional events: 1/ I burnt down the transformer by accidentally disconnecting one of the secondaries 2/ I had to make another transformer in order to continue my experiments.

So, sleep well tonight. OU is still not here.

~A