Dispatch scheduling policies offer a computationally inexpensive approach to many scheduling problems as an alternative to more processor intensive search algorithms. They are especially useful in dynamic situations where problem solving may be temporally constrained. However, dispatch heuristics have also been effectively used for guidance within more intensive search algorithms, expanding their applicability well beyond simple myopic job or task selection. In this paper, we present a new crossover operator for genetic algorithms (GA) where a permutation representation is employed. Our new operator directly integrates problem-dependent knowledge in the form of a dispatch scheduling policy into the crossover step of a GA which is usually a problem-independent recombination. Our novel crossover operator, Heuristic Sequencing Crossover (HeurX), recombines elements of M parents into a single child and is specifically designed for steady-state GAs. We empirically demonstrate its effectiveness on a strongly NP-Hard scheduling problem known as Weighted Tardiness Scheduling with Sequence-Dependent Setups. We compare our approach to a generational GA using a problem-independent crossover operator. We show the potential power of integrating problem-dependent knowledge via a dispatch heuristic into what is traditionally a problem independent problem solver.