Well I’m first exhausting some promising regions of the search space which should complete in less than 2 weeks. After that I strongly suspect a solution doesn’t exist (for the column grouped space I’m searching).
If it were just a matter of a few thousand dollars of computer time (say, less than $5000) the money would already be spent and I’d have an answer.
We’ll see, I may build the tooling to distribute the search and enlist help from others interested.
It’s only been about 2 weeks since I was able to drop the runtime from “age of the universe” levels to just decades.
Posting it here will almost certainly lead to a "May the best clanker win" contest, you realize!
If someone wants to beat me to either a solution, or proving no solutions exists, then by all means :-)
I think it's an extraordinarily hard problem computationally, even with exceptional theoretical backing.
Where people may be able to beat me is if no solution exists-- there may be some highly nontrivial, but findable unsatisfiability argument.