Reduce the power of the sensing device way way down. There is plenty of MCU and low power analog stuff these days that can likely get the current requirement down to less than a few dozens of mA instead of the 1000 to 4000 mA that you have quoted.

Now use an LDO at the load to provide VCC for the MCU and put a FET switch in the supply line to the device such that the MCU can switch its supply lead on and odd using MFM encoding (50% duty cycle guaranteed) and have the receiver end measure the current and recover and decode the MFM to receive the digital data from the MCU. Should be easy.

Michael Karas