Yep the intent is to use the leftovers as a guide for the 12th word, but your way works fine too.
The box is just a little checkbox to mark off to affirm you've gotten the final message, in case you didn't get 144/144 in doing so, or got all 144 but missed the message due to not writing out the list.
Hmmm. The most similar game I can think of is LOCK for PS Dreams. (Although I haven't played it myself, I just watched Keith Ballard's play-through.)
I don't play a lot of word games or puzzle hunts, so everything else that comes to mind is just normal puzzle games with good epiphanies -- Linelith, Öoo, Slicecraft, Pâquerette, Bee Magic, N-Step Steve, Insight, A Monster's Expedition, etc.
In terms of books, ABDEC might be the most similar to 12 WS (consistent rules, fleshed out over time) but it is fiendishly difficult at one point. Oh, and the excel-based puzzle Rainbow Challenge / INTAO 🟥🟧🟨🟩🟦🟪⬛ seemed excellent, though I got stuck halfway through, and it's structured such that the rules change for every puzzle.
