This is the prefect time to roll your own search. I’ve done almost the exact same thing with Fuse, and it worked great.
Keeping things in sync isn’t too hard. You can see how I did it for Elasticsearch:
firebase-search - Index your Firebase collections to Elasticsearch and/or Algoliagithub.com
I suspect the Firebase team will figure out an integrated search solution at some point, but who knows how long that will take.
Let me know if you run into any more issues. I’m happy to help :)