Many traditional query optimizers support setting query configuration hints to steer the optimization process. Using these hints efficiently to decrease analytical query runtimes has been successful for learned models. However, the most successful approaches use queries annotated with their best optimizer hint beforehand. Even though learned models can significantly decrease query runtimes, the query annotation overhead outweighs their results. Since most use cases cannot allow for significant time investment before deploying a solution, related approaches become impractical. In this paper, we delineate the shortcomings that emerge from the currently used approaches in hint set prediction. We identify that their labeling techniques and increase in the number of supported hints render them infeasible. To overcome that, we propose FASTlabel, a novel labeling algorithm tailored toward the supervised hint set prediction approach FASTgres, which efficiently traverses the hint set search space for each query while supporting multiple hints. We show that our labeling strategy reduces the amount of query-hint set combinations that must be evaluated substantially, solving the current exponential scaling issue. Additionally, our experimental evaluation shows that FASTlabel makes supervised hint set prediction feasible, reducing the inherent labeling overhead of supervised learning approaches substantially.