I don't really have a problem with getting enough steel made. I have a problem with completely unrealistic ferrous metalworking. You need as much flux as you do ore. This is not how it works in the real world. The in-game recipes are completely silly. Flux is mainly used for removing carbon, coke is used to add it, yet you need both, for both steps? Nope. That is not how ferrous metalworking works. Before the reverbatory furnace, the fuel used in smelting iron would introduce too much carbon, yielding pig iron as the direct product of the first step. Another step is required to make usable, non brittle wrought iron. If just the right amount of carbon could be removed in this step, steel could be made in small batches. More commonly, carbon was added back into wrought iron in a third step. The amount of flux used was minimal in comparison to the amount of ore used.
Dwarf Fortress technology is high middle ages tech, in general. At that time in the Western world, the most common process was the bloomery for producing sponge or pig iron. This was refined in a finery forge by heating and hammering to squeeze out the inclusions, producing wrought iron, or careful management of the process would result in removing the correct amount of carbon to produce steel. Outside of China, no better way of making steel was known at the time. The puddling furnace and the cementation process weren't introduced into Europe until the 1500s.
You don't have the details of early iron/steel production quite right here. Bloomeries did not introduce significant carbon into the iron, by avoiding heating it to its melting point. The sponge was hot-worked to remove most of the remaining slag and silica impurities from the iron. Because the iron was never brought to its melting point, no flux was used in a bloomery. Until the introduction of the cementation process in the 1500's, European steelmaking a hit-or-miss process. Sometimes if a bloomery were able to be run hotter than normal, the iron would partially melt. When this happened, you would get a sponge which had steel or pig iron in it along with the wrought iron. Later, finery forges and puddling furnaces were used to remove carbon from pig iron (produced in blast furnaces from ~1200CE in Europe) to make wrought iron. Steel could also be made in this way, but without a reliable way to control how much carbon was removed, the quality of European made steel remained low.
Blast furnaces were able to heat the iron above its melting point. Molten iron absorbs carbon much more readily than the still-solid iron in the bloomery process, so when using a blast furnace, you end up with pig iron. Blast furnaces for pig iron production are generally loaded with a mixture of crushed iron ore, coke or charcoal, and crushed limestone or dolomite. The coke/charcoal helps to control the amount of carbon in the resulting pig iron, while the limestone acts as a flux. Limestone and similar fluxes do not remove carbon from the iron. The flux does make the iron flow a little more easily, and causes a larger portion of impurities like silica and sulphur compounds to separate from the iron and remain in the slag.
The earliest method of creating consistently high quality steel originated in India, possibly as early as 300BCE. The exact method of steel production is not known today, but based on a combination of what information does survive, combined with analysis of surviving samples of early Indian steel and modern attempts to recreate the process, it was most likely one of 2 different crucible steel processes. One candidate process involves mixing pig iron, flux, and an oxidizing agent (possibly crushed hematite or another iron oxide) in a crucible, and melting it. The oxidizing agent combines with carbon in the steel to form carbon monoxide which escapes as a gas, while the flux helps to remove slag and other impurities from the mix. The 2nd candidate process involves mixing wrought iron, pig iron, and flux in a crucible, putting a layer of sand or crushed glass on top, and melting. The sand or crushed glass melts, and floats to the surface, creating a barrier against carbon escaping or getting into the molten metal, while the flux aids in the mixing of the iron and pig iron, as well as helping to separate out impurities and slag from the metal.
In addition to the crucible processes mentioned above, by the 11th century, a variant of what would later be called the Bessemer process was in use in China. The bessemer process produces a very low carbon steel with few impurities, which is easier to convert into steel of the desired composition than wrought iron.
The DF process for making pig iron is similar to the blast furnace method, the primary differences being the amount of flux used, the use of iron bars instead of raw ore, and the lack of a specialized blast furnace. The DF process for making steel from pig iron is similar to the 2nd listed process for crucible steel, with the main difference being that the crucible steel uses molten glass as a vapor barrier, and does not add additional coke/charcoal to the mix.