https://www.gold.org/about-gold/gold-supply/gold-mining/how-...
If people know it's going to be released, it doesn't make too much of a difference exactly how long you are going to take.
(Unless you go really, really slow.)
I'm not so sure: The price of gold depends on an estimate of future supply. If a company can successfully mine an asteroid for 5 grams of gold in 2025, many people will be worried about a massive increase in gold supply over the next 50 or 100 years. They would then dump their existing holdings of gold and crash the price.
In reality, some entity will get the first metal asteroid, and have a monopoly for a while. But only a while.
I don't understand your arguments for no price drop. To me the facts are simple: Price is set by supply and demand. When supply increases by 10x or 100x, prices will fall dramatically.