Do you believe in this catalytic cycle? Has it been proven? In addition, I do not fully understand the question since there is a cleavage of the O-D bond! Please keep also in mind that, in presence of the phosphate base, methanol might become (partly) deprotonated.
Have you tried CD3OH or CH3OD to confirm it's the C-D bond only and not the O-D bond? It's not necessary BDE-driven because the chemistry is 2-electron processes, not radical chem.
Beta-D elimination (and the corresponding beta-H elimination) has been seen before at Pt and Pd. See the intro and discussion of my Pt paper, we cite a Pd example (see Figure 3), check that Pd paper our and forward search it to to see other examples. Article Reductive Elimination and Dissociative β-Hydride Abstraction...
If you need access to the article, I can send you a copy.
We have done CD3OH and CH3OD experiments. It was published in below attached publication. Not only, my work M.Beller also published similar kind of mechanism for his C-O cross coupling reaction. My question is, why the deuterium exchange was not happen from weaker O-D bond. Why it's not dominating the BDE process. Is there any specific reason?