This will be my last post on this topic because I think that we are restating the same points here without breaking any new ground.
As my final point, I note that you are using hoarding = non-monetary-use = has on impact on price. As I pointed out before, this definition is a bit idiosyncratic. Hoarding is usually used to mean a monetary use.
All uses of gold, whether monetary or non-monetary, participate in the price system. Because some gold is held in non-monetary form does not mean that the owner does not have a reservation price for their gold. For example, the owners of jewelry some times sell it for melt. There have been a lot of articles about this in various media. People own jewelry that they no longer care about so they sell it. As a hypothetical example, suppose that you owned an electronic gadget that had 0.1 oz of gold. You might be willing to sell it for $120 for the scrap value of the gold if you didn’t like the device.
Non-monetary use of gold competes with monetary use. Gold can move back and forth between these uses. The price mechanism is similar to the way that the price system works with international trade - the same good tends to trade at the same price everywhere, plus or minus transport costs. In the case of gold, non-monetary gold and monetary gold would have the same price plus or minus refining and assaying costs to transform the gold.
There is one market for gold. All of the gold in the market is subject to the same analysis, whatever it is used for - that is the marginal analysis of price based on reservation demand. As gold is used for one purpose (monetary) or another purpose (non-monetary) there are costs to melt and refine. These transform costs are reflected in the price system.
If gold were used as actual money, then in all liklihood the purchasing power per ounce would have to increase because gold would need to take the place of peoples’ cash balances now held in the form of fiat money. As the purchasing power of gold increased, gold would flow back from non-monetary use to monetary use because the market price would hit the reservation price that people had placed on their non-monetary gold. This fact contradicts your point that non-monetary gold is not part of the price system. Non-monetary gold is part of the price system, it does compete with monetary gold and it is on sale on the market, at somer reservation price.
The distinction between monetary gold and non-monetary gold is not really so signficant. It is not more significant than the distinction between gold that is cast into Kruggerand coins and gold cast into Sovereign coins and gold cast in to 1 oz bars. Gold is not really different than any good on the market for which there are multiple uses. Because gold is transformed, not destroyed, as it is used for different purposes, when it is used for one purpose, it is always available for other uses. Those other uses are at all times competing for its current use. The price point where gold would be purchased and transformed for one use to another depends on the reservation price of each individual.