I hadn't thought of doing it your way.
Got your PM orthocoil; thanks for reminding me to get back to the subject. I was a little heads-down trying to make improvements I could share with the gang here. Unfortunately, I'm not there yet, so I'll just have to show what I got and let the winner take the pot.

Anyway, attached is my version two LLT.
I put five labels on the image we can use for reference:
A. Small air core primary
B. Heavy gauge shunt winding
C. Secondary winding
D. Pickup winding
E. Laminated silicon steel C-Core
The reason I don't have this device detailed on my workbench is that I'm not at all clear how to properly drive it. At the moment I have a spark gap (impulse) system connected but it has some problems that I need to work out.
The tiny air coil primary (A) seems to need some help. Inserting soft iron welding rods is the easiest means so far. Without some sort of core here, you have to use very high frequencies well outside the range of the of core (E). My thought is to make a C-Core out of ferrite rod--place the rod through the coil and the other half outside the windings. This may lower the operating frequency without lowing the reluctance so much the main core (E) no longer grabs the majority of the CEMF.
The (B) winding is a bit hard to see. I believe it is 4 AWG, just shunted together. I couldn't find a proper size piece of copper pipe that I could form around the bobbin, but as-is, seems to do the job.
The secondary (C) windings are just speaker wire, zip cord. This allows me to gang the two windings in parallel or series (bifilar) and is far easier to wrap than just a single wire. It's 18 AWG and can handle a few watts if I ever get to that point.
(D) is the test or pickup winding. It has a couple of uses. I can inject power into this winding and observe the core is shunted via the (B) winding. I can also use this winding to detect ever slightly ringing within the core. The more I look at it, the more it seems I should have switched positions between (B) and (D). I may try this once I get my drive methodology figured out.
The C-Core (E) is a power core purchased from Bridgeport Magnetics, capable of about 3000 watts. Used here in the LLT, it provides the low reluctance magnetic path for the CEMF
If we walk through this device, starting with (A), we see that only the secondary (C) encloses the primary (A). So there is no possibility of induction into (B) or (D). So if we get any induced EMF, we should see it in the secondary (C). Now with just pure potential in (C), nothing should be observed in (B), (D) or (E). However, if connect any sort of load to the secondary (C), this winding will now create a magnetic field in opposition to that of the primary (A). This magnetic field created inside the windings (C) will funnel itself to wherever the lowest reluctance is; that being the core (E). When it does so, it induces an EMF in both (B) and (D). Lets assume (D) is left unconnected and concentrate on what happens in (B). The (B) winding is now induced and creates another magnetic field that is opposition to the field generated by (C). Fortunately for us, this magnetic field will aid the field created by (A) and the cycle repeats. This is Lenz Law executed twice per initial induction event.
Hopefully this is sound logical thinking and from what I can tell so far, appears to behave as I have suggested. Things get difficult when you consider coupling, frequency response, core saturation and the many other factors power engineers deal with. I haven't progressed beyond the toddler stage thus far and have restricted my testing to simple impulses where I can see a partial effect manifest. I'm mostly stuck at the moment and I think I know why, but haven't a good plan yet for a version three. The speed of impulses I need to get any power transfer from (A) to (C) is so fast that (E) can't even respond. It is way outside of its frequency range.
My thought for future improvement is to use multiple cores (E) and use a similar core for (A). With this, everything should have an equivalent frequency response. What will happen though is some of the CEMF will make it back to the primary, but it will be strictly proportional to the number of cores utilized. So with one primary core and nine locker cores, only 10% of the CEMF will get back. Doing this may however complicate the coupling even more. It's a difficult problem to solve.
This is what I have. It may be something worth pursuing, maybe not. If anyone knows a straightforward way to get nature to cooperate, I'm all ears.