I also tried downloading the theme and placing the zip file into the themes folder in the 3ds, but the problem still persists.

There's your problem. Whoever made the theme didn't properly convert the audio to what the 3ds supports. This happens most of the time because they followed an ancient online tutorial telling them to set the music to mono, which is notorious for causing this issue. I made a lot of 3ds themes in the past and only had this issue 1 time where I miscalculated the Hz for the music. It could also be that the file size is too big but that will often result in music not playing at all on the 3ds. These are all the cases for screeching with custom themes.

The theme creator really ought to take a look at the discord server for theme plaza, they have a full tutorial that is up to date.