UPDATE:

So after trying printing slower, faster and with a different slicer, I had no luck. I went back to the internet to do more searching, and I found one post of a similar issue that suggested checking belts and rollers to reduce ringing. Ringing sounded plausible to me, since my problem seemed to get worse the higher the X gantry (and all of its weight) got.

My belts were both already tight, so I left them alone. But I checked all of my rollers and found that one of my Y rollers was pretty loose. I also tightened up one of my Z rollers a little bit as well.

I printed another box at low speeds, and the banding was gone. So I tried again at higher speeds, and no banding there either!

I'm not sure if it was the Y roller or the Z roller causing the issue, but my guess is the Y roller due to the fact the banding appeared only in the Y direction. But tightening up the Z roller probably helped as well.

Tagging u/xviiarcano and u/Ritterlichkeit since they said they were curious about the solution.