Fun problem. When solving with Gecode, you might want to add the annotation `:: domain_propagation` to the `all_different` constraint (https://www.minizinc.org/doc-2.6.2/en/lib-stdlib-annotations...). Sometimes a good idea, sometimes not.

If you can extract some instances you could send in your problem to the MiniZinc challenge (https://www.minizinc.org/challenge2022/challenge.html), preferably with several instances with varying complexity. The benefit for you is that it is a good way to ensure that your particular problem is tested for a lot of solvers, and may be used for improvments of solvers in the future. The deadline for this years challenge problem submission is 6th of May.