Implanting that rocket engine - after a successful “gentle and accurate landing” of the engine, its guidance package and fuel tanks on the rapidly spinning and tumbling rock! - will be very, very difficult.
Once landed, then as you point out, it needs to be securely implanted into the rock (or metal and rock or gravel or whatever is found) so the rocket thrust actual gets aimed where it needs to be pointed so the impact point is moved to a “safer” position for future orbits.
My opinion? Measure, then blast it with a big (50 to 100 Megaton) into 2 or 3 smaller blobs. Each blob will have a new trajectory. Each impact will stop higher in the atmosphere too.
Stopping the (probably multi-axis) rotation of a rock could be done a few different ways. A small nuke would work. An impact from a different, smaller hunk of Solar System debris would work, and would be within current technical limits.
https://freerepublic.com/focus/chat/4296982/posts?page=22#22