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Short answer is "you can't" as the 4-20mA current loop is an analogue signal and the Pi does not have any direct analogue inputs. You can, however, add a device called an Analogue to Digital Converter (ADC) to your Pi that will let you then take analogue measurements.
Typically you'd "drop" the current loop output of you sensor across a 100 or 120 Ohm ...
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This is not a complete answer but a suggestion to narrow down the problem. All transfer methods you have used are using the same buffered input/output API of the operating system so it shouldn't make a difference. To test low level direct writing of random data without using buffered I/O you can use dd assuming disk partition /dev/sda2 is mounted at /mnt/p2/:...
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