Well, keep in mind that Akka Persistence and Akka are very different things. Akka Persistence specifically is the journaling-persistence approach; it sounds like that's a problem for you. But Akka more generally works fine with traditional RDBMS, within some contraints. In particular, if your database's API is blocking, then you'll want to confine the DB access to Actors that are designed for that purpose, and put them within their own dispatcher so that those blocks don't gum up the rest of the ActorSystem.
Besides that, though, it's pretty straightforward -- I've had my system in production for several years, with Actors on top of MySQL, and it's never been a problem...