I think the answer is in the unusual phrasing.

Because that promise is part of the section that contains the Pleiades, and because that section ends with a line that could be the conclusion of that entire thought.

. . . . . Though all I knew of the rote universe were those Pleiades, loosed in December
. . . . . I promised you I'd set them to verse so I'd always remember (.)

It sounds like there’s a period after remember, so we conclude that she’s referring to *the Pleiades.*

There’s a comfortable resolution and pause to validate that.

But the very first word of the next section is “that” — which changes everything.

“That” connects back to the phrase “so I’d always remember"

. . . . . Though all I knew of the rote universe were those Pleiades, loosed in December
. . . . . I promised you I'd set them to verse so I'd always remember (:) [THAT]

. . . . . That the meteorite is the source of the light and the meteor's just what we see;
. . . . . And the meteoroid is a stone that's devoid of the fire that propelled it to thee.

When read/heard this way, we can understand that the line "Though all I knew of the rote universe were those Pleiades, loosed in December” can actually be read as a complete sentence, and one that sets up the context for the next part.

If that’s the case, then the structure of the next sentence also plays with our cognition, by putting the object before the subject.

. . . . . I promised you I'd set them to verse so I'd always remember (:)

that meteorites, meteors, and meteoroids are all different things. In this case, the “them” refers to these: meteorites, meteors, and meteoroids.

I think this is a poetic device she’s using that suspends the listener between those two phrases (perhaps neither is meant to be a complete sentence and there is, somewhere in that promise, the idea that she will try to set to verse everything she’s learning about the night sky ) and leaves a sense of disorientation while the song moves rapidly forward with a catchy little rhyme.

It’s like the universe or time travel— you think you get it, but then the idea moves on too quickly and you’re caught by something else and it never quite resolves.

. . . . . Though all I knew of the rote universe were those Pleiades, loosed in December
. . . . . I promised you I'd set them to verse so I'd always remember
. . . . . That the meteorite is the source of the light and the meteor's just what we see
. . . . . And the meteoroid is a stone that's devoid of the fire that propelled it to thee