since the impulse of L1 is at the resonant speed of L1 (its a half wave, a half period),
and it is created in a resonant condition (L1 is charged up with a magnetic field, then quick the mosfet switch is opened)
the L1 is resonant.
When it is close coupled to L2 the current draw is reduced. but the magnetic field of L2 is amplified by the impulse.
since L1 is resonant, and L2 is resonant, and both are close coupled, it is best, to make L2 resonant at a lower octave of L1's resonant frequency (twice the L1 impulse duration= period of resonant frequency).
L3 is parallel resonant, and thus also a lower octave of the L1 impulse.
I still am not convinced, the L3 should be parallel resonant tuned. Best would be, to not tune it down by adding parallel capacitance at all.
just let the coil ring by itself ( grounded on the outside rim).
Then L1 impulse is a half period of L3.
but for the L1 impulse to travel this fast (short duration) through L2, it should not exceed L2's resonant frequency.
I do not mean the tuned down L2 series resonant frequency, but, L2's own series resonant frequency (without added capacity), as this limits the maximum speed of the impulse (due to L2 capacity).
Since L2 is cloase coupled to L2, L3 needs to have a lower resonant frequency, else it would be to fast, and demanding a to fast impulse for L2.
Solution is to use smaller diameter wire for L3 (but equal copper mass between L2 and L3).
So a 1,5mm2 L1 and L2, with a 0,75mm2 L3 (or 4mm2 L1 and L2, with 2,5mm2 L3; or 2,5mm2 L1+L2, with 1,5mm2L3)