>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.

This. Not all ejecta from asteroid/comet impact is vaporized. Some is launched at escape velocity mostly undisturbed[1]. Mars both cooled first, giving it a leg up to allow biogenesis[2], and has lower escape velocity, making easier for rock chunks to be launched from there to Earth, rather than the reverse. From thousands of impacts and billions of rock chunks ejected from Mars in the early solar system, the successful delivery of a single viable microbe would be enough to seed Earth.

[1] https://fire.biol.wwu.edu/cmoyer/zztemp_fire/biol345_F10/pap...

[2] https://arxiv.org/pdf/astro-ph/0403049