Ok, putting an LED in in place of an incandescant lamp changes too much!
You’re correct, with the big coil it just might operate off of local radio power. But that definitely was not the case with the original. 1000 crystal radios couldn’t light the incandescant lamp.
Well, I've been thinking of this. Why does the coil have to be oriented East-West? When you used a crystal radio, once you got it tuned in, there wasn't any directional component except to orient it in relationship to the transmitter. Let me think about this. I also have to go into Sacramento to get some wire. I've got a boatload of magnet wire but it's all on metal bobbins which is effectively a core and I'm too old to be winding coils.
If I can buy two or more, 120vac solenoids and cut away the cores, I've got everything else, my only home choices are output transformers and toroid power transformers and those cost me big bucks which I'm not going to destroy for this.