I'm a newbie to woodwork and surprised myself by successfully creating an even Black Japan stain on some Tasmanian Oak. I then decided to finish it with Danish Oil. Somehow I arrived at the decision to brush on a heavy coat of the oil and leave it until it dries. A week later the wood has an inconsistent tacky/ gummy and shiny finish and the grain seems to have risen. I've read that wiping down the surface daily with mineral turpentine or methylated spirits will eventually remove the tacky surface. The issue is that the wood is also stained and in the small section I tried this on the turps stripped about 25% of the stain.
TLDR: What can I do to remove the tacky/ gummy Danish Oil finish from Oak without removing the stain?
Stained and Oiled: