Well done for trying to find the new owner, in my eyes that effort should clear your conscience of anything you want to do with it.
My missus once found a very chunky gold curb bracelet at a petrol pump, after talking with the station and making arrangements the owner was found and my missus personally handed it over, they thanked her.
Another occasion her relatives found a little black velvet bag in a posh hotel safe and it was filled with jewels, again owner was found and they got a thank you, neither times did the owners offer anything for returning their expensive goods, I say that from a standing that I would have made sure the honest individual was rewarded for making the effort and returning my goods.
Well done for trying to find the owner. I am surprised Breitling wouldn't keep it until the owner emerges via insurance claim or similar ?