Griz,
I'll add my welcome to the forum.
I strongly recommend you follow a version of Pahoo's advice by trying different finishes in small patches in the barrel channel of your stock, where they won't be seen when the gun is assembled. Your piece of wood looks beautiful, but it won't absorb or be wetted by any two finishes in exactly the same way as any other piece of wood.
A cabinet maker taught me to apply Danish Oil and similar wiping varnish finishes using 320, 400, and 600 grit wet/dry automotive sandpaper in three successive coats, used in that order. Otherwise, follow the can instructions for keeping it wet and when to wipe off, etcetera. This produces a finish that resembles a tung oil finish, but is much quicker to apply.
I highly recommend to you and anyone else interested in the topic that you buy (and read) a copy of Understanding Wood Finishes (subtitle: How to Select and Apply the Right Finish) by Bob Flexner, Fox Chapel, pub., 2005. ISBN 978-0-7621-0680-6. This is a big format paperback that goes through each type of finish and its pluses and minuses. It explains varnishes, shellacs, oils, stains, dyes, waxes and other finishes in great detail with extremely well reproduced photos taken in the right lighting to show what is being discussed.
The book has lots of tips and Myth/Fact sidebars. Some of it quite surprising. I did not know that no matter how many layers of linseed oil you put on wood it would be quickly penetrated on contact with moisture and smudged (light blotch). Tung oil, on the other hand, has good water resistance but takes about a dozen coats to develop a satin finish, with several days drying between each coat. So it take a month or more to apply properly, and then some drying and hardening time beyond that before you use it. I didn't know that most wipe-on finishes with the term "tung oil" in their name have no tung oil in them at all. They are varnishes and not oils, anyway. They just produce a finish that resembles a properly applied 12 layer tung oil finish.
The book is easy reading with illustrated discussion and tips for application methods. It goes well outside gun stock finishing, since it's not aimed at us in particular, but having some background in what things finishes will and won't do will quickly narrow your choices.