Recently appearing from Jonathan Draper is his “The Old Testament in the Didache and in subsequent Church Orders” in Siegfried Kreuzer et al. (edd.), Die Septuaginta – Orte und Intentionen (WUNT 361; Tübingen: Mohr Siebeck, 2016), 743-763.
The title is slightly misleading, in that beyond the Didache the only church-order discussed is Constitutiones apostolorum. Nonetheless this is a useful preliminary study.
On one minor, but significant, point, I find myself persuaded. Namely that Didache 9.3 does not make reference to Matthaean tradition, as I had always supposed, but is rather derived from Leviticus 22:10, which concerns those who may eat of Temple offerings. For Draper, this is the result of seeing the Didachistic community as a sanctified community. Is it Anglo-Catholicism which leads me to suggest that some sanctity also attaches to the food?