I managed to fit the small inductor into the other dimmer. It fits, but only just.
Please don’t look at my shoddy soldering job. Also, I did tape it up to be safer.
This definitely lessened the chopping noise from my speakers, but unlike with the other dimmer, the noise is not gone entirely. I guess it’s because I tested the specific inductor with the other dimmer and lights, and because this dimmer runs right next to the amplifier.
Still, the noise is much less than before and only noticeable because I know it’s there, and even then I can only hear it when I turn the volume way down. I might revisit this in the future, but for now, problem solved :)