I think you're asking the right questions. Gold and the dollar need to be compared to at least one additional commodity to triangulate stability, but ideally you should compare multiple commodities with substantial historical data. Similar to your suggestion, I might include cement, steel, copper, wool, maize, sulfuric acid, sodium hydroxide, and coal. This includes construction materials, industrial metals, plant and animal farm products, commodity chemicals, and energy. Everything in the collection has been produced and traded on a large scale for at least 100 years.

Once you have the basket of items to compare, you can see how different prices correlate over time. If gold is more stable than the dollar then you should see a stronger positive price correlation coefficient, with lower standard deviation, between gold and the members of the basket of commodities than between the dollar and the basket members. That is, if 1 gram of gold buys 150 kilograms of steel today, and 1 dollar buys 2 kilograms of steel today, the gold to steel ratio should deviate less over time (past and future) than the dollar to steel ratio, and the changes should be positively correlated: steel moves up when gold moves up, steel goes down when gold goes down, and by similar amounts. You can even perform the correlation exercise with pairs of mundane commodities: maybe it turns out that sulfuric acid tracks other commodity prices more closely than dollars or gold, and cautious savers should actually clamor for an acid-backed store of value.

Even without running the exercise over a full century of data -- which I don't have to hand, alas, else I would have -- I don't think gold is going to perform too spectacularly. The tremendous gold price volatility around 1980 was not, so far as I know, reflected nearly to the same degree in mundane commodities like coal and wool. It may well be that gold holds its value better over long periods if you smooth the time series, but people can't (directly) trade in smoothed time series: someone who decided to convert all their saved dollars (or steel, coal, wool...) to gold in July 1980 would have taken a heavy loss only a year later and would have needed to wait 10+ years to recover anything like their previous holdings, converting back from gold to useful commodities. The same specious arguments (scarcity, durability) sometimes advanced now to justify an irreversible value increase for gold were being touted just a few years ago about real estate. Value is always relative.

Let's get back to silver dimes and silver as a value store for a moment. Mercury is rarer in the Earth's crust than silver, it's been known since antiquity, it's shiny and dense, it can be neither created nor destroyed, and supplies and production rate from mining are limited. It even has more desirable properties for commerce: since it's a liquid at room temperature, it can be subdivided for any transaction as needed, down to the limits of the traders' scales. So why do the traditional coinage metals have their privileged position, if (as sometimes claimed) precious metals are "natural" monetary standards rather than reflections of human psychology and historical inertia? Despite all these wonderful attributes of mercury which should make it equally or more precious than silver, it currently trades at less than 5% of silver's price, and no nation has ever backed its paper notes with mercury.