This paper looked at ways of achieving high power-to-weight ratio for harvesting power from a 50Hz overhead line.
https://findresearcher.sdu.dk/ws/portalfiles/portal/250674676/EPE_2023_Advanced_Magnetic_Energy_Harvester_for_Charging_Drones_from_Overhead_Powerlines_final_version_.pdf

It clamped a toroidal current transformer to the line and used power electronics to convert to DC for charging.

It used synchronous methods to maximize the power draw taking into account the saturation characteristics of the core.

To me, it seems power-to-weight ratio might also be increased by having an intermediate high voltage DC bus that is stepped down.  The high voltage of the DC bus would allow for a higher power output given the magnetic field / current limitations.  For this setup:
1. Is it advisable to avoid core saturation?
2. Would power factor correction on the secondary side significantly increase the throughput, and if so, is it advisable to use AC capacitors with the pickup to create a tank (at 50Hz....), or use an intelligent H-bridge to phase-lock the voltage and current (like this: https://www.ijert.org/research/simulation-of-closed-loop-ac-dc-converter-for-power-quality-improvement-IJERTV4IS031036.pdf)
3. Is kW range power transfer feasible without degrading the power-to-weight ratio significantly, even if only for a short time (<1min)?

Some parameters (let's say for a target charging power = 200-300W):

 - approx 1kg toroidal air-gapped pickup as per above study. 
 - line current ranges from 50 to 200A. 
 - let's say a 600VDC bus so that 1200V semiconductors can be selected.

I am not asking you to design my circuit.  I am not 'being lazy'.  The purpose of this project is not academic / commercial, or even hobby. It can be assumed that the power harvesting is legal. I don't care if this question is 'bad' in some way - I've spent enough time trawling through the net and trying to excavate knowledge from my BE (EEE).  If you would like to help, then please do :)