in contrast, a toddler equipped with an ion thruster & a modest quantity of xeon propellant could achieve enough delta-v to attain cheetah-escape velocity, provided the initial trajectory during the first 31 hours of the mission was through a low-cheetah-density environment

That initial trajectory also needs to go through a low air density environment. At normal air density near the surface of the Earth that ion thruster could only get a toddler up to ~10 km/h before the drag force from the air equals the thrust from the ion thruster.

The only way that ion thruster might save the toddler is if it was used to blast the cheetah in the face. It would take a pretty long time to actually cause enough damage to force the cheetah to stop, but it might be annoying enough and/or unusual enough to get it to decide to leave.