>the energy required to kick up a rock to a trajectory where it will hit Mars (or vice versa) is orders of magnitude more than the energy required to vaporize all nearby life, so we've got a pretty big problem already

Not necessarily. Something like the asteroid that killed the dinosaurs would have created temperatures at the impact point high enough to vapourize everything but probably also chucked a lot of more distant stuff into the sky that didn't get as hot.

Here's a Discovery channel 'simulation' of a large impact chucking stuff up https://youtu.be/bU1QPtOZQZU?t=67 Not sure it's very accurate but it gives an impression of the sort of thing that may have happened.