High-speed steels (HSS) are widely used tool steels, as they exhibit application-specific favorable properties such as superior hardness, which are usually the result of pronounced microstructures consisting of carbide inclusions within a martensitic matrix. HSS contain a variety of different alloying elements posing challenges with regard to recyclability and, in addition to that, the carbides make use of critical alloying elements such as tungsten (W) or molybdenum (Mo). Hence, reducing the number of alloying elements and substituting the critical with less critical ones, such as vanadium (V), is necessary for more sustainable HSS. To assess the influence of microstructure morphology and phase properties on the overall performance, a virtual, data-driven workflow is advantageous. The validity and efficiency of such workflows depend on (i) a minimal yet expressive set of microstructural design parameters, (ii) appropriate 3D microstructure reconstructions, and (iii) numerical simulations that capture the mechanical response with high accuracy. Here, a workflow is presented which takes into account higher-order statistical descriptors, as used in so-called statistically similar representative microstructures, as they are expected to be necessary to unambiguously describe HSS microstructure morphology. However, their high dimensionality makes them unsuitable as design variables for the later optimization. Therefore, we propose an approach to significantly reduce the design-parameter space by distilling characteristic features from the higher-order statistical measures. Still, an artificial three-dimensional microstructure needs to be reconstructed from the designed statistical descriptors, for the framework MCRpy is used. With reconstructed microstructures at hand, numerical micro-indentation simulations are performed using a contact implementation in the finite element framework Ferrite.jl. This allows the hardness of the designed material to be computationally assessed, such that an optimization scheme can be employed for the identification of the particular material design leading to the highest hardness.