This is an area where "solvers" are heavily under utilized. For the absolute fastest solution, bespoke implementations are almost certainly required. However,

This is an area where "solvers" are heavily under utilized. For the absolute fastest solution, bespoke implementations are almost certainly required. However, translating Sudoku and N-Queens into a similar problem that you can feed into a solver can get you a long way. Even better, you can move that solver into whatever language gives you the best optimizations that you can work. Even better, there are almost certainly optimizations in common solvers that you don't want to deal with implementing on your on.