Hmm. Perhaps use a long ferroelectric rod, held crosswise. It's a capacitive ballast in series, working a bit like a metal antenna, except it's insulating. So, no explody flaming events if it should touch across the 300KV line.
Too bad that it's all based on 60Hz. Weight of copper/iron coupling components goes inverse to frequency. A 100KHz power system gives enormous coupling for the same weight of components, when compared to 60Hz. (It's almost like they were designing it to make power-theft difficult!)
Also, note that the EM field of a big 3-phase line is mostly concentrated between the lines, and out to about one line-spacing around all three. In other words, the three lines act somewhat like coax or twisted-pair, each partially shielding the others, with the fields dropping rapidly to zero at a distance. Must needs fly really close.
A conductive plasma connection would work better. With x-ray lasers "burning a path," you could tap tens of kilowatts and run quite large motors as well as the lasers. So, a propellor-lifted flying saucer with built-in death-rays. Idea: pulse your x-ray lasers at 15KHz to provide high frequency switching supply, for low-weight supply electronics, and AM car radios go crazy from the supply harmonics, plus the 'plasma tweeter' ultrasonic output makes dogs howl whenever it's nearby.