Bronze is about the oldest metal men ever fabricated ~ 5000 years ago! There's no mystery to it.
The mystery is what the composition of that case is ... in order to match the color if you want to fill with weld then reshape the lug.
You might contact a good yacht or ship repair shop if you are near a port. Propellors are bronze, often get damaged, and have to be repaired. It's worth a try if you can't live with the current situation OR the price of the Rolex case replacement.
On second thought, looking to your repair estimate "the heavy impact to the case middle" implies there is more damage than what is shown on the lug. Is that true?
I had a pal bring me a Rolex once that he'd more or less thrown across the locker room when swinging his jacket. It impacted on the tile floor and the case was enough egg-shaped that I couldn't get a round crystal to fit into it.
If that's what happened with yours I see no other alternative to replacement. Maybe a second-hand / used watch (saving your movement for later if it still runs).
Sorry
Cazalea