Hi,
Pics would help. you are absolutely certain it's cherry, not a look-alike?
There used to be a chemical application for ebonizing cherry that was indelible. It could be planed off it you took enough wood.
It used something like bi-chromate of potassium or some such.
There are two kinds of wood bleaches: oxalic acid (for mineral based staining) and the two-part liquid (peroxide-based ) used for organic stains. You may have to try both, but I'd start with the oxalic acid because it's less harmful to the wood, IMO.
Can't say if linseed oil would darken it "enough" becuz I haven't seen it.
Casey

You can maybe just keep on wiping down with stripper, though I guess Casey is suggesting that if it is ebonized, no more colour will come off. So if you try wiping with a white cloth/paper towel soaked in the stripper you're using (or lay the soaked cloth on top for a while, then wipe), you'll see if you can get more out. I use a stripper called EZWay that doesn't require water clean-up, and it does a great job of that last bit of colour. On the woods I've worked on anyway.

KarinL

Without photos, I'm just guessing, but it could be pigment from a stain that is still lodged in the pores. If so, you might have some success applying a coat of shellac, letting it cure, then stripping it off. The shellac may bind to the pigment and the original stain binder and pull it out. It may or may not work, but would be worth a trial.

Cherry pores are very small.

Is is considered a 'closed grain' wood.

Are you sure it is not some other wood?