Bright side of things is that there's strong evidence that landslide tsunamis rapidly weaken with distance; they can be incredibly high close by, but lack the ability to propagage thousands of miles, one of the reasons most tsunami researchers think the whole ridiculously overhyped "Canary Island Volcano collapse would wipe out the East Coast" scenario is a crock.
You get a much more confused, complex system of waves from a landslide that dampen each other out over long distances.