I'm not at all expert enough to be definite about the Barbet, so these are just comments.
Firstly, Usambiro should have a full black breastband - this is one of the features that distinguishes it from plain D'Arnaud's. But this bird doesn't.
(Also this bird has no red vent, a feature shared between the species, just a hint of orange in the vent area. Therefore I wonder if it is a young bird, and judgements of 'green-ness' might be delicate.)
(And, incidentally, I'm not convinced that the 'diffuse greenish wash' on the head is such a great ID feature; in my limited experience (I've seen both birds) the apparent head colouring depends very much on lighting conditions.)
Secondly, Usmabiro is not on the
birdlist for Manyara. (The linked list does recognise the split, as Usambiro is on the Serengeti list.) The distribution area in Stevenson and Fanshawe also doesn't stretch to Manyara.
In Northern Tanzania, the ssp of D'Arnaud's should be boehmi, I think, which has a fully black (i.e. not just streaked) front to the head in the adult which is quite striking in full light. In this photo, however, this area is behind a branch, so it's difficult to judge. Usambiro has some black streaking in this area, which can look like a light black cap, but can also be invisible in bright light head on.