Though Burmese are a good donor for the Tibeto-Burman in Burmese, it seems pretty clear now that I have Tibetan samples that the Bangladeshi samples are a bit more Tibetan-skewed than these Burmese samples. It may be that the early admixture into Bengal was from a Burmese population that had admixed less with the Austro-Asiatic substrate of Burma.
Note that this confirms the Austro-Asiatic populations have a totally different (more southern) East Asian ancestry source.