Nobody can just pick up a set of checkering tools and recut checkering without many hours of practice. There are so many idiosyncrasies that one must encounter before working on something that cannot be "fixed" if messed up. There are people on this Forum who can recut checkering.
As for the refinish part. I can only tell you how I do the work. After stripping and fine sanding the smooth surfaces, I dilute a small amount of Tru-Oil with paint thinner and apply to the stocks, let it soak in and using compressed air blow out the excess from the checkering before curing. I then apply two coats from the bottle with my finger to the smooth surfaces and let cure. Do not apply any more finish to the checkering. I then use steel wool to take off the luster since factory stocks were satin finish, not gloss. I use no stain and do not believe that the factory stained their walnut either? An example is below.
Last item is that I use a Q-tip dipped in Acetone to wipe down the medallion.
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