Got it! [LAYR]DATA makes sense now. It's data3 and data4 from .j2l files in a single section with no break between them, except instead of four tiles long, the words are sixteen tiles long. That's why I thought the sections of sixteen blank tiles were missing -- it wasn't the layer I was looking at, it was the pieces of the layer. The frontmatter of the section is a length long, a short (MAXTILES-AnimCount), another short (number of words), and then another short that may always be zero. Now all that's left is EMSK, MASK, and a few miscellaneous shorts and longs here and there.

ETA: I've put what we've figured out so far up on the ERE.