You shouldn't have to lose any land for this. trim back any branches the goats haven't, right to the fence so the wire doesn't catch on anything, put the elecric fence right up to the netting, they should respect it enough not to climb on the fence, they might do a little upright dance trying to reach if there is any higher overhang, but that gives them shelter anyway, which would probably annoy him :-).
I use one strand round the inside of my stock fence, they will carefully graze almost underneath it but never reach over.