Do not apply another finish on the oil unless it is oil... It will do no good and it will look ugly. The barrel channel does not have any finish or sealant of any kind. Problem is that sealing it differently from the outside of the stock might make the inside and outside take up water at different rates. That is when warping happens.
Apply oil finish to the barrel channel and you will not be sealing it. Apply spar varnish and it will seal it so the water comes from outside only. In wet conditions it will tend to warp toward the barrel.
I would oil the barrel channel and use a liberal coat of paste wax everywhere, including metal below the stock line.
On a side note, in general matte finishes are achieved by adding bad stuff to good finish. It is easier than applying the finish properly and buffing to the desired sheen. On stocks especially matte finishes should never be used. Start with gloss, always, then matte with rubbing compound and oil.
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