runner: I don't have a good answer but I do have some sympathy for your plight.
As the others have mentioned, staining with any oil base stain isn't the best way to go but as I recall, most stains have trouble with the CVA stocks.
At least, I have had trouble with them. The wood seems to take the stain in some places and absolutly refuses to take the stain in other areas.
I don't know what kind of white wood they use but whatever it is it is difficult to work with.
Getting back to the water/alcohol based stains, they work better than any oil base stains because you can apply multiple coats until you get the darkness you want. With oil based stains, once the wood has absorbed all of the oil it can, your stuck.
If you want to try one of the water based stains you will have to totally "kill" any and all of the oil that's soaked into the wood. Any oil at all will prevent the water based stains from soaking in.
To kill the oil, you may have to soak the stock with something like MEK, Acetone or Disk Brake Cleaner.
All of these are really bad for your body so don't breath them any more than you have to. Also, the MEK and Acetone are explosive so keep them away from any source of ignition.
Another way of getting the oil out is to call a professional wood refinishing shop. They can totally distroy the existing oil without removing any of the wood. They might also have some good words of advice on how to get the CVA wood to stain more uniformly.
zonie