I have modified a little the original compose-key in order to be able to use it with my japanese chromebook.
It works great as long as I am on the physical keyboard, but I have noticed that when I go into tablet mode, I always get an american layout displayed on the on-screen keyboard, while the pressed key is indeed mapping the japanese layout correctly.
This is how I changed the manifest, but perhaps I am missing something so the on-screen keyboard is displayed correctly?

    {
      "name": "Compose Key (for Japanese keyboard)",
      "type": "ime",
      "id": "compose_key_jp",
      "description": "Adds Compose key functionality to the JP keyboard.",
      "language": "ja",
      "layouts": ["jp"]
    }