The G3VM-41 has a maximum forward voltage of 1.48 V. If you use Schottky diodes in the bridge rectifier, they will add around 0.4 V each, so two of those.
That means that you will need at least 2.28 V as the voltage across the current transformer.
You could just put two of the 57PR1831 transformers in series.
Alternatively, you could use one of the higher-rated transformers, and put more than one turn of the wire that you are trying to sense. The higher rated ones are larger, and have a larger voltage that they will supply.
If you use the 57P1833, it is rated to 150 A. If you wind 10 turns of the input wire around that, the 8 A input current will only have a 100:1 ratio, so the output will be 80 mA. The transformer is rated to have a 43.3 Ohm load, which gives a voltage of 3.464 V as a maximum. That should give you enough voltage to operate the G3VM-41, after any losses in the the Schottky diodes and a resistor.
That means that you will need at least 2.28 V as the voltage across the current transformer.
You could just put two of the 57PR1831 transformers in series.
Alternatively, you could use one of the higher-rated transformers, and put more than one turn of the wire that you are trying to sense. The higher rated ones are larger, and have a larger voltage that they will supply.
If you use the 57P1833, it is rated to 150 A. If you wind 10 turns of the input wire around that, the 8 A input current will only have a 100:1 ratio, so the output will be 80 mA. The transformer is rated to have a 43.3 Ohm load, which gives a voltage of 3.464 V as a maximum. That should give you enough voltage to operate the G3VM-41, after any losses in the the Schottky diodes and a resistor.