Cylinder Head Question

4mm is a lot of movement against spring pressure, and would indicate valve guides/stems that are basically destroyed. So I am wondering if we dealing with mis-recognition of parts here? You said "The pieces with the springs." I wonder if you mean the 'rocker arms'? They also have little springs seperating them. One side of them will have a little rod coming up to it (pushrods). If that is what you meant, then the repair requires replacing them, and finding out why they were not getting enough (or any) oil. You can do this yourself, with decent junkyard parts, rather then pay $800 for him to do it.