The magnetic field has a precise form that must not be changed by any other source of magnetism
I'm already explaining it here. The overunity arises, when the magnetic domains don't change their orientation - but size periodically in analogy of repeated evaporation and condensation of water droplets. Which is also reason, why the magnetic field must be arranged symmetrically toward center in Sweet's billets. The bifilar coil can just pickup the irreversible changes in A-field intensity instead of B-field which is reversible. Many other overunity devices utilize the same mechanism and they utilize many types of ferromagnets at kilowatt scales - so that the Floyd-Sweet process is not exceptional in any way and there is actually no difference in strontium and baryum ferrite behavior and also no magic in barium ferrite preparation. This process must be very robust - or we couldn't drain large energy and COP from it.
In general, if we surround some coil with pulsing electromagnetic field (i.e. this one fast changing intensity - not just orientation) with bifilar coil, any power induced in it will not induce back electromotive force, so it could be drained for free. Once the induced power will get larger than the resistive and capacitive wastes within coil (which can be eliminated with proper construction of it, i.e. elimination of skineffect and capacity of its winding), then the overunity will be reached during selfresonance of the coil. And this effect works even in vacuum, as it doesn't require presence of any ferromagnet. The attenuating effects of ferromagnet domain could be easily replaced with increasing the voltage at the coil.