Have you tried Hydrogen Peroxide? I've used it to remove nail polish from carpet, but I've heard it also works on ink.
It takes a while - you moisten the stain with peroxide, work it in with a toothbrush, let it soak a while to break down the stain, then blot it out with paper towels. (It's important to blot and not rub.) If ink comes up on the paper towels, just keep repeating the process till the stain is gone. You can also put towels over the peroxide moistened stain, then cover it with folded towels and put a stack of bricks on it for several hours.
It took me quite a while, but I successfully removed about 1/4 bottle of bright red fingernail polish from tan carpet, with no damage to the carpet and no evidence of the stain.