Sync new purchases to iPod Classic

I recently refurbished an old iPod Classic, and purchased some albums in the iTunes Store (yes, it still exists!). Once I found out that most iPod Classics are capable of playing Apple's lossless format, ALAC, I really wanted to sync them over to experience this heretofore unimaginable audio clarity. However, even though I could download them, the albums refused to show up in the sync list.…