Can you turn it off while you are operating? Pool cleaning doesn't have to be done continuously, does it?
Also, I bet the standard bypassing approaches would work to some extent. Another thing (the first thing I thought of) was sheathing the wires externally in something and grounding it.
Considering the risk to any kind of device posed by lightning, as well as the possibility somebody digging might hit it, if its buried - putting cable in conduit seems like its likely a good idea, and probably required by electrical codes.
One thing that might be interesting, is seeing what capacitance does to the moise.. If the cable is currently a wire lying on the ground (sounds like it may be) try taking a yard or two of aluminum foil, in essence making a big long "feed through capacitor" along the line, and then grounding it to see if it reduces the noise (I'm not suggesting that asa permanent solution, just as a test!) You could use an RTLSDR and the "rtl_power" binary the osmocom driver comes with to visualize and that way, get a quantitative idea of what is happening spectrum wise. It can sample huge swaths of spectrum (if you had two RTLSDRs you could run it to sample from below the AM broadcast band to >1700 MHz, and dump its findings to a CSV file, then you can use the data viz app of your choice to examine your data. There are scripts that can turn it into charts, frequency and amplitude (mapped to color) over time.