Of course, this requires that the aliens have precise knowledge of the distance to our solar system, and the Sun's motion through space. For an advanced society, that might not be too much to ask. But the kicker is this: they will know that, during the transit, our world is somewhere in front of the Sun's disk. So they could use a mirror array to focus their signal on that disk, thus reducing the power requirements for signaling to less than 10 watts, comparable to a bicycle headlamp! Yes, the mirror would now be a mile across, but it could be made up of a few small, cheap, and simple individual reflectors.
In other words, with a collection of mirrors, a small laser, and a computer to run it all, a knowledgeable and entrepreneurial extraterrestrial could produce detectable signals with only as much power as a handful of batteries could supply. No mammoth antennas, and no beefy transmitters are required. The broadcast could be an alien science fair experiment.
It's interesting to imagine that attempts by extraterrestrials to locate other intelligence in the Galaxy might be made not by officialdom in massive societal programs, but by the personal efforts of the young and the daring.
What she found there were three archetypal figures, emerging from popular comedy: the Yankee, the backwoodsman, and the minstrel. Each member of "the trio," as Rourke often called them, took recognizable form in the 1820s and flourished until the Civil War. More important, she wrote, they remained at the heart of "a consistent native tradition," which she traced through the classic American writers — Whitman, Hawthorne, Henry James — and up to the modernists of her own day, including T.S. Eliot. "Humor has been a fashioning instrument in America," Rourke concluded. "Its objective — has seemed to be that of creating fresh bonds, a new unity ... and the rounded completion of an American type."