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I did some work in that direction recently (also the Exact Cover variant, which turns out to be easier). It makes some pretty pictures, like this[^] (Set Cover variant) and this[^] (Exact Cover variant).
Spoiler alert: I solved it with ZDDs. Runs in about two seconds. Half a second for the Exact Cover variant.
Is that interesting enough to write an article about? I've got some stories about trade-offs and design decisions, and pretty pictures of the results.