"According to one poster here (pretty sure it was either Nick or Alex), the Moon was created by an incredibly large impactor (this, btw, was already an accepted theory), but the result of that impact stripped the Earth of a chunk of mantle, leaving a gap the planet has been trying to fill ever since. Sort of like a slide-puzzle, where you need to slide pieces around a board to create a picture."

I don't think Alex or Nick would say that.
I believe the "most accepted" theory is that Proto-earth was hit by an "incredibly large impactor" (around the size of Mars), it's core partially merged with the Earth, the rest of it plus some of Earth's Mantle was ejected into space. The Moon formed out of this ejecta. This happenned about 4.5 billion years ago.
The Moon would cool and form a crust before the Earth (the oldest rocks have been found on the Moon). The Earth would be completely molten after being hit by this "incredibly large impactor" so it's unlikely that it left any scar/impression on the surface.
After the Earth formed a crust (and assuming no later impactor re-melted it
the entire surface) impactors could make impressions which could still be visible today.

"Seems reasonable, therefore, that tectonic shift in the habitable zone of a star might be pretty rare."

This could be true.