You could add strictfp
to the classes in Java-land. Elsewhere I doubt there is a good solution. I have to wonder why you would need this precision though. Most apps shouldn't be relying on the animation system for app logic.
Posing a skeleton is deterministic in that it does not depend on previous frames. For a given animation time, the pose will be the same (to within float precision). You could use fixed point for your animation time and I'd expect that to be good enough. Note this may change as we add physics features, which depend on previous frames by design.