This would cover the beams, of course, but it would keep the wainscoting look. Over the past year, I have seen gray marks on the nails holding the plasterboard wall onto the studs. I bought the house four or five years ago and fixed it up, and did everything I thought I was supposed to do. No one can tell me what causes those gray marks. Well, I can certainly try to tell you, with an informed opinion.
Moisture is the cause and it is no one's fault, really.
Then mildew will grow on that wet spot, or dust or dirt will land on it and stick, both creating those gray spots. That dust or dirt is no reflection on your housekeeping. If the bleach has no effect, it is dirt, which can be washed off with any cleaner. To try to prevent this from recurring, ventilate the house twice a day for a few minutes to release excess water vapor.