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SUBMIT YOUR IDEASome might call this a solution...
Well this one was certainly interesting. I couldn't wrap my head around math to sort the tools by their appropriate row and column, so I did it manually. Kept getting errors trying to generate this as a temporary PDF, but HTML and PNG worked fine, so I went with PNG. Attached.
Great challenge. I learnt a lot there. My solution isn't quite as fancy as some of the others on here but it meets the brief I think.