The first batch of CTs I used saturate at 500mV. At 60hz you cannot get more that 0.5V out of the CT at any current.How about rectifying the current through the coil?................. You could use Schottky diodes.
The larger ones I got saturate at about 1V. Will not light an LED but will turn on the B-E junction of a transistor if wired across the transistor. I could not make it work if I used a diode and transistor in series.
I have found lager yet parts that will light a 1.5V red LED. By now it became better to get a Shelly PM.