Have you tried wiping the entire stock down with a Damp Mineral Spirits rag to see if it rids it of the Tacky feel?
If this works, I'd then wipe on some Lo-sheen Tung Oil on the dull area. After drying you could then buff down with a lemon oil polish.
If you use the polish first, you'll have problems getting the Oil of choice to adhere.
The problem with spot repairs using RLO/BLO are just what you've pointed out.
A stock that was originally dunked in a heated vat of RLO....
Then having who knows what put on it over the next 70+ years.
Just wiping RLO/BLO on in no way will yield same results as the dunking.
Little info here: BLO Relic and Military Surplus Firear
---------- Post added at 01:25 PM ---------- Previous post was at 01:23 PM ----------
Nice Color Blend BTW