For me, "nearly" and "almost" point to the near-reality of the statement, whereas "hardly" points to a quite different reality. Cf.
1. I was nearly hit by a bus.
2. I was hardly hit by a bus.
3. I was almost hit by a bus.
4. I nearly won the lottery.
5. I hardly won the lottery.
6. I almost won the lottery.
Thus in #1, the accident might have happened; but nothing hit the speaker.
In #2, however, something hit the speaker; but it wasn't anything as serious as a bus. (You might say #2 in a slightly irritated fashion, if a small child on a tricycle ran into you, and a passer-by expressed extreme concern.)
In #5, on the other hand, the speaker won something; but perhaps only £5 (certainly not the lottery).
So for me, nearly/almost aren't quite as symmetrically related as the positive/negative distinction would suggest.
Other members may have other views, though!
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