Thanks R0J0hound, that does work. Good old lerp :)
I'm not sure how I would go about applying this to everything on screen. It works well when you just have one or two items, but gets complex fast when you try to speed everything up. Unless there is a scalable way of doing this I might just have to put this feature on hold.
It appears that some libraries like Box2D already take continuous collision into account (I assumed this was why the bullet behaviour was working because it implemented this), so it would be nice if this could be added to C2 Ashley if you are listening *bats eyelids*