I've been thinking about this for a while. I don't think there is going to be a simple solution to move away from EntitySpaces and move to EntityFramework. But the approach I would, and probably eventually will take, is if you haven't already, add an interface to each of the methods in your Business logic that inherits from the data classes and include every method you need.
Now, add a Database First EF model and create new business-logic classes for each entity/model to inherit from that interface you've made. Then you know every method that requires re-writing in EntityFramework(LINQ/Lambda). It's a slow process but this way you can do the migration over multiple release windows, slowly moving everything over, referencing the new EF business-logic models as-and-when you have time (and of course, any new tables can use EF straight away).