I hear ya, Seafox! The stock from my Huntsman ML is currently bare and soaking up stain, a little at a time. I use Varathane oil-based stain, and wipe off a goodly part of each application in areas where I know the stain will "take". When it's dry, I apply more in areas that are light (using cotton swabs or Q-tips). Wait, let it dry to a hard surface, rub it down with a clean shop towel, repeat the fill-in step as many times as required to get a fairly even appearance, and live with the imperfections.
I think the factory finish is semi-opaque and applied quickly with a spray, then UV-cured. If the wood wasn't so proud, I'd just leave the factory finish in place. But there is a shapely stock hidden in that "pallet wood" somewhere, and I am determined to find it. Dremel, sandpaper, more sandpaper, and finally the struggle to get a decent walnut-colored finish on that light wood.
To see a fabulous stock-refinishing outcome, look up Fred M's .257 Roberts project. I can't find the darn link, but I'm sure you're better at computers than I am -- If you can't locate it, PM Fred and he'll send you the link. He got a beautiful cheekpiece out of a factory stock.