Thanks guys - that was my suspicion. We have just one big index that keeps growing. On our old (now test) instance running an old version I have cron job that just deletes the index once a month.
I will see what it takes to get this set up properly. I can google myself, but it could be helpful if you point me to a resource that goes through setting up the indexes/templates/policies from scratch in a way that will support ilm? Much appreciated!