Bayesian phylogenetic methods offer various models that would be especially suitable in the reconstruction of textual traditions, but text-critical applications of phylogenetics to date have generally not taken advantage of these features. In this paper, we offer a way forward for text-critical phylogenetics. On the side of theory, we highlight multiple Bayesian phylogenetic models and discuss their relevance to textual criticism. More practically, we show how TEI XML collations of textual traditions can be encoded to facilitate robust analyses using these models in BEAST 2, with the teiphy Python package mediating the conversion from TEI XML to BEAST XML. Finally, we give a proof of concept for this approach, showing that the results of BEAST 2 analyses of a sample collation of the Epistle to the Ephesians under different clock models cohere with established findings on the textual tradition of this work.