So it turns out that I really need the location data in the base class to make life much, much easier with game object messages. And with other things as well.
Of course I did change quite a lot, but it's not that bad I guess. What I will keep is the Mover class, nothing wrong with that. It just makes moving possible to proper classes. Yet the base class should have the location data for above reasons. You don't have to save the location, it can be reproduced for objects that are only in the map.
I hope I get this mess resolved fast, because it's getting on my nerves.