I havent tried this yet, Im slow and think about things alot but if I can change the frequency of the two sets of primary's I may get some reflection going on, create a standing wave.
Not sure but fun to think about then try 

Iv been reading Gotoluc and trying to understand reactive power and what causes it how its created in the transformer I have a hunch it has to do with the bemf of the coils, I'll be studying that as well,
We live in perilous but exciting times
keep up the good fight
dave

after measurement corrections; I didn't look at both ends of the secondary when I measured it, it looked like the near end was going positive; after grounding probes and signal generator grounded, it is more apparent that the current induced by a rising current is in the opposite direction.  This would make two north poles approaching...

to go back to a static case, a approaching north pole results in a current that is also a north pole and is repulsive to that magnet.  When the north pole moves away, the current generated that is a south, which attracts the magnet, and makes the magnet will be harder to move away.  (current directions reversed if south is applied, but still to first repel the approaching magnet, and then attract; evident by eddy currents actually dropping a magnet on a surface generates a pole that keeps that magnet away... and conversely will 'stick' to the magnet, not allowing it to move away)...


Back to coils, coil A has current A rising, coil B will have current B rising; a rising current B in coil B would make a rising current A in coil A... this appears to be a self reinforcing condition; even though the effective magnetic poles are inversed spacially...


Coil A has current A falling, coil B has current A rising;  in coil B rising current A will cause a rising current B in A... since current A is diminishing, adding more current B will help it diminish faster...; this too is self reinforcing; so the more the current falls, the more it is applied to fall..


it would appear that a falling current has more chance to oscillate itself... the faster the current_A in coil_A falls, and coil_B, with a rising current_A makes a rising current_B in coil_A(opposing the already falling current_A)... ?the backwards current coil overtake will overtake current A... which will then be a rising current B in coil A, which is a rising current A in coil B, this was already the current in coil B... but then again it's probably a continuous limit;
As current_A in coil_A approaches 0, current_A in coil_B approaches max, then starts falling itself(least capacitance/most resistance)... a falling current_A in coil_B makes a rising current_A in coil_A... This will first cancel any excess current_B from the rising current_A in coil_B; and a rising current A in coil_A will make a rising current_B in coil_B; again reinforcing current_A in coil_B to go to 0... leaving Coil_A with current_A and coil_B with current 0


So the falling oscillation is really more than the capacitance of the scope probe accounts for.


A single coil though is like the magnet approaching and leaving... and a coil itself is similar to other momentum force...ie a current in motion will stay in motion;... with very little inductance (a straight wire) the current decays faster; and this is measurable by looking at the circuit with low resistance points so you can see where the potential differences are.


if have a positive/negative power source, when you disconnect a coil across those points, the first event is that the end previously connected to positive becomes negative and the end previously connected with negative becomes positive, which then rings down.... if there is nothing there; a null capacitance fill fill instantaneously and look like a reverse current; was trying to setup a model circuit to demonstrate all alone...  It's the case of chokes that reminds me of this... they flow with a current, if a abnormal spike is encountered, it is smoothed (depending on size and inductive characteristics, but assuming enough inductance...)... which means that if it was a low dip, it would keep current at a similar level, if it was a high peek, then it would lag back and keep the same current....

In the sim; before I added a dioded capacitance, the empty capacitance of the switch filled in a tick, and the whole force looked like it was going backwards with a huge amount of negative force... but this clearly demonstrates a slow rise in current acorss the inductance, and disconnecting the power, the continued forward current of the coil. to the point that the wire off the diode is a negative voltage (extra electrons, coming from ground, carried in momentum).


Simulator to show forward momentum...


----
Edit: I'm done rambling here too... but I will finish this with thoughts after sketching some things...
Back EMF ringing proposed doesn't happen. The rising current would stop rising in the secondary when the primary has no current left... so given infinite capacitance, the current would just transfer completely from one to the other....
Though I suppose that's why twisted pair works better... two wires rise and fall faster than one alone.  (3 4?)

Look at where the reactive power shows up, right as the coils are switching, big clue 
If reactive power is bemf from the coils that means ac is not working perfectly with the magnetic rise and fall as I thought and leaves room for improvement 
We'r gonna figure this out and when we do its gonna be on like donkey kong 

QuoteDuring part of the cycle the current is positive while the voltage is negative (or vice versa), as shown in the shaded areas; the current and voltage work against each other, creating reactive power. The device produces work only during the time represented by the non-shaded parts of the cycle, which represent the circuit's active power.

http://electrical-engineering-portal.com/electric-power-quality-lighting-1
The primary is fighting itself, the bemf from each side of the primary is opposing instead of aiding.
We can fix this.

This is exactly why this model didnt make sense its right the voltage and amperage are pulsing from one side then the other its fighting itself, and not working together.
The grid frequency is 120 cycles but we only see 60 thats because half the time its producing voltage and half the time current but only using one primary is causing it to fight itself.
Well maybe not completely right, need to study it more.
I just love a good anomaly dont you