The only way to replace the transformer with an active circuit would require very manyf devices (for example, junction transistors) in parallel. It would be huge and consume a too much power.
The way to replace the transformer is to use a coil with about 500 turns.
If I understand, the proximity effect is like the skin effect, but resulting from the magnetic field produced by current in other turns. I do not think that this is an issue in a 500 turn pickup coil since the normal resistance of the wire would dominate except at very high frequencies.