Actually, 'cheating' on 12-tone is sort of 'canon'. Webern was the odd one of the original serialists in that he never did any fudging on rows/matrices, while both Berg and eventually Schoenberg himself were known to do so.
There's also another way to do this than the gridded-out matrix method, too. On "Euphony IV" (https://daccrowell.bandcamp.com/album/euphony-iv), I experimented with what I call a 'quantum matrix'. With this piece, there are several voices playing through individual tetrachords, two playing through hexachords, and a few more that were capable of playing all notes in the prime row, with all of the behavior being controlled through a generative system that still weighted the pitch classes equally, that being the key underlying criteria for the method. By doing this, in essence the generative process is accessing ALL points in a given matrix at once, but 'collapsing' the observation when the process sounds a note. The results were actually VERY satisfying; parts of it remind me in some ways of a 'switched-on' variant of the denser parts of Schoenberg's orchestral writing in "Moses und Aron".