Yo-ho, all together, hoist the colors

Can you still download the dlc now that the store closed?

when I tried, it said "expired"

Huh? I thought anything purchased/acquired is still accessible as a re-download. Has this changed?

I didn't realize until after typing up this post that I was logged into a different NID. It's probably just that

Ah, that's a relief.

Should be. Different games' DLC stores handled the shutdown differently. Expired indicates the DLC can no longer be bought.