I think you can keep right on using the tung oil. I've used it several times on maple guitar necks and it works very well for a moderate sheen and a smooth, warm feel; I don't know any reason it wouldn't work on walnut too.
As mentioned, wet-sanding with it will help fill the pores. Apply a coat, sand it in, wipe off any major excess, let it set up, start over. When you like the color and it doesn't want to absorb any more, burnish it with worn denim.