I would say that you need a 4th axis on a machining center to do that work.
When you say perfect fit how much tolerance does that permit? Is this some kind of a pump? How did one part wear out while the other one did not? Can you verify zero wear on the good one? It is very elusive to expect a perfect fit if some wear is present on the part that will be reused because all the reverse engineering in the world will not predict the wear factor that could be waiting to spoil the job.
Will you have to harden the new part?
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)