I figured it out! Thanks for all the help.

I'll come back to this and explain, but I wanted to say I got it going (and now I want to get the rest of my bike running!)

 

So: The key insight (or a big one, anyway) is that the lower throttle cable attaches differently to the grip than the top cable does. Once I unscrewed it, I saw that the nut itself is attached to the threaded portion, allowing it to screw directly into the hand grip without needing to rotate the grip.

By cracking the grip, and adjusting the lower cable portion like Ern suggested, I was able to wiggle out the cable from the track, then back it out of the grip entirely. Ditto for the lower cable. Then, I could spin the grip around the upper cable elbow to thread it back in correctly. After threading the top cable back in, the bottom cable was simply a matter of turning the nut/threads to work it back into the grip.

Tighten everything back up, and it seems to work well.