...Something a tradesman who has a good reputation wants to avoid is doing bandaid repairs. This could be the tip of the iceberg as far as damage is concerned, and to repair a small section may be an invitation for more repairs being necessary later and reflect on that tradesman's work.
That being said, and not being a mason by trade, I would think that it would be possible to remove stucco and replace it for a lot less money that doing a stone or brick face on the chimney.
Next time take a picture of a NH plate and tape a copy of it over your license plate, and then hang camo netting between your house and the lake. Might help!
