I doubt, that paralleling FETs in an reactance driven HiZ? application is worth the effort. The noise figure of an Hi-Z FET Amplifier ist primarily dominated by the thermal noise of the Gate bias Resistor of 22 Megohm which is much higher, than the FET noise. It may make sense in Low-Noise Audio applications, where the source impedance is low, but IMHO not as an e-field probe for RF-reception.
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For the use as an short monopole e-field antenna, the common mode choke at the output is "stealing" the earth/ground reference, which is normally provided through the braid of the coaxial cable and which is necessary to pick up the voltage? (U = E x heff) induced in the probe by an electric field. With an CMC at the output, a separate earth connection to the amplifier ground is mandatory, otherwise the amplifier cannot "measure" the potential-difference between probe and earth, because it lacks a ground reference.
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More reading:
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regards
Fred