For the record, a precise disproof of Lemma 3.4 seems to be in this preprint of Amar Hadzihasanovic [Diagrammatic sets and rewriting in weak higher categories](https://arxiv.org/abs/2007.14505). Further recent developments involving diagrammatic sets are gathered in the book [Combinatorics of higher-categorical diagrams](https://arxiv.org/abs/2404.07273) by the same author, and the preprint [Diagrammatic sets as a model of homotopy types](https://arxiv.org/abs/2407.06285) by Chanavat and Hadzihasanovic.