My takeaway: modeling problems in minizinc correctly is exceptionally difficult for non-trivial problems. You can model it correctly, but you'll likely still need to add additional "constraints" that improve the performance of the solver to the degree where it's even remotely usable to solve real problems.
It's a really interesting tool, but one of the reasons we thought it might be useful for this problem is so that non-technical people could easily change the constraints and play with the costs for different operations. I don't think it's particularly good for that, at least in this problem domain.