Might be time for a pro. This is work which require a "touch". But trying to feather out the dings is not probably a good approach.
One technique is to use a wet towel and a hot iron. The wet and steam can swell the wood a bit, which then is left to settle for a day or too, before final sanding.
I am not a pro on that technique, so I would do some more googling to fill in the details.