I put the 15W load in series with the L3 coil and its parallel capacitor.
it didnt work, as expected.

L3 should not be loaded, just tuned to L2, so it can be in series resonant mode. probably best, when L2 and L3 voltages are equal magnitude.  if L2 and L3 are equal size coils (inductance and capacitance)

When L3 is in LMD mode (voltage and current in phase) then L4 should be connected, outside rim of L4 to inside rim (resonant) of L3
outside rim of L3 to ground

with TEM resonance, the impulse  on L2 series resonant sine, helps build up the magnetic fields of l2 and l3, in a transverse manner.
This is hard for the impulse to do, and it starts to ripple.
parallel capacity needs to  be added to L1 to prolong the duration of the impulse, so it doesnt ripple.
impulse voltage goes down, and needs higher input power to reach equal voltage.

the higher tuned resonance is LMD.
Here the impulse helps to build up the longitudinal in phase voltage and current. which is much easier for the impulse to do, as the impulse already seems to be in LMD mode. (not sure as L1 is also resonant)
The impulse does not need to be prolonged in duration, can be made very short (no capacity added in parallel over L1).

Still not sure if L3 is out of phase voltage and current with TEM resonance mode, should be so.
L3 is definitive in phase voltage and current with LMD resonance.

This topic is done the double primary research is concluded.

I proceed at:
Tesla extra coil

Already have success!
the extra coil holds 15kW unloaded