However, using a 2-sig-dig constraint to restate 12,450 to 12,000 makes quite a bit of real world difference if the units are "ounces of gold."
Only if you can in fact measure the difference. If you can’t, they may very well be the same number, or it may even be possible that the “12,000” ounces of gold are more than the “12,450” ounces of gold.