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Quantum memories play a key role in facilitating tasks within quantum networks and quantum information processing, including secure communications, advanced quantum sensing, and distributed quantum computing. Progress in characterizing large nuclear-spin registers coupled to defect electronic spins has been significant, but selecting memory qubits remains challenging due to the multitude of possible assignments. Numerical simulations for evaluating entangling gate fidelities encounter obstacles, restricting research to small registers, while experimental investigations are time-consuming and often limited to well-understood samples. Here we present an efficient methodology for systematically assessing the controllability of defect systems coupled to nuclear-spin registers. We showcase the approach by investigating the generation of entanglement links between silicon monovacancy or divacancy centers in Si⁢C and randomly selected sets of nuclear spins within the two-species (13⁢C and 29⁢Si) nuclear register. We quantify the performance of entangling gate operations and present the achievable gate fidelities, considering both the size of the register and the presence of unwanted nuclear spins. We find that some control sequences perform better than others depending on the number of target versus bath nuclei. This efficient approach is a guide for both experimental investigation and engineering, facilitating the high-throughput exploration of suitable defect systems for quantum memories.