Well there it is.
It's funny, I was grinding Classic for a while, then decided to switch it up and try Trophy Rush. This was pretty much the method I used to get all custom moves (along with playing Smash Run). I tried that with headgear, but it just wasn't happening, so I just stuck it out with Classic for the most part until that moment.
In my first Trophy Rush run, I did shit and only got 3 custom items, and then I scrolled down through the rewards page, and I see a headgear icon with "NEW" on it.
I'm pretty much done with single-player in Smash 3DS. Feels good.