John,
I'm pretty sure you really mean "Carbon Tet", short, for tetracloride. It was a useful clorinated solvent, and was very useful for any type of welding on used fuel containers. A thin layer poured on the bottom of said container, with a barely cracked air line bubbling in it, and ALL danger of explosion/combustion was eliminated. But, one's safe yearly exposure was about zero, so, it had to go.
I fall into the camp that the soaking over time oil removal methods are a bit tough on old wood. I've had good results with regular gel paint stripper with a quick alcohol or acetone wash to remove what is raised up by the stripper, followed by gentle heating and covering with whiting. Keep alternating until satisfied.
I've had some oil that never seemed to come out, no matter what was tried, as well. Not sure what to do in those cases, but, I replaced the wood.

Best,
Ted