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That was a pretty fun read. Discrete optimization is still a huge challenge that many companies still face today.

So...is it naive to think that I can create something similar with MiniZinc (or an equivalent package)? Or will it take too long to even get an answer without CUDA? This seems like a pretty fun weekend project!

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It really depends on how many constraints and variables you're optimizing for. Because this problem is NP-hard, I'd bet you could make a more naive version that solves some easier ILP problems, but scaling it up probably requires quite a bit of optimization/good heuristics. Definitely seems like a good learning experience if you're interested in algorithms though!

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