I believe FUN HOME's new album will be eligible, but for you EGOT counters out there, I doubt Tesori or Kron will be counted among the nominees. The Grammy rules state that "lyricist(s) and composer(s) of a new score are eligible for an Award if they have written and/or composed a new score which comprises 51% or more playing time of the album" so, since FUN HOME received an album release previous to the current eligibility period and there is not a significant overhaul to the score, only the producers of the album, the engineers/mixers, and any principle vocalists (I would guess Malone and maybe Cerveris.)
THE KING & I may also rear its head here, as the Tony winner for Best Revival, but I think the other nominees had far superior albums. ON THE TOWN especially is a masterpiece to me as a recording, and ON THE TWENTIETH CENTURY has Chenoweth's name (to my knowledge, Cheno has never won a Grammy so conceivably a win here could put her an Oscar away from EGOT.) Sting could conceivably wield significant stature within the music industry for a LAST SHIP nod, too. Don't count that out.
But HAMILTON is currently slated for a September release, which should slip it in under the eligibility rader. And there seems to be a considerable recency bias at the Grammys, so I have every expectation that everyone's favorite monolith should be our favorite here, too.
Words don't deserve that kind of malarkey. They're innocent, neutral, precise, standing for this, describing that, meaning the other, so if you look after them you can build bridges across incomprehension and chaos. But when they get their corners knocked off, they're no good anymore…I don't think writers are sacred, but words are. They deserve respect. If you get the right ones in the right order, you can nudge the world a little.