Ground the fence through a capacitor. .01uf to .1uf at, perhaps, 2.5kv should work. Depending on the operating frequency of the station and the length of the fence, you may need to ground the fence in several places.
Several items from experience at a 100 kw AM:
Fence wire on insulation-prone posts (wood or cement) may have wire junctions which are physical and not soldered. Make sure each stretch of wire is grounded and the joints may oxidize or be loose.
One piece of wire was a wavelength long. It did not like being touched. We insulated it at a random spot and grounded it.
A section of mesh fencing and a gate surrounded the entrance side of the property. In the construction process, the engineer had run a copper strap about 20 cm wide from the copper sheets at the tower base out to the entrance, and the fencing was connected to this with clamps that were then soldered since the ground was copper and the fence was whatever they made galvanized fences out of. That was mostly done to prevent maintenance people from getting RF burns as the lobe towards Buenos Aires was close to 200 kw.
This is an electric fence. It can't be directly grounded.
The ampitude of the electric fence pulses must between 3KV and 7KV to overcome contact and ground losses. If I'm not mistaken the price for a capacitor that you mentioned is pretty stiff. I had understood that you had a similar problem in Tampa. At the site in question, there is no sign of such mitigation. The RF burns are pretty severe. Would it be possible to speak with you? As you can see speaking with some one is more efficient than E-Mail. It seems that David misunderstood me. This is not an ordinary fence, but an insulated wire that provides a shock to livestock.
But hold on here.. It's an electric fence. Who cares whether you get zapped by 7KV electrical or RF? It's supposed to hurt if you touch it.
If you want to breakup the RF, I'd put some "J" type torroid cores in series to each wire every 50 feet or so. Those torroids will block the RF, but pass the pulsed AC.
But the fence systems I've seen do pulses, so there is no chance of an animal or person getting electrocuted. Otherwise, you have a real danger when it rains or if the land is naturally wet or moist.