After looking unsuccessfully for a Bb MKVI bari locally, I took a chance and purchased the Thomann Low Jazz about a year ago. The horn needed a trip to the tech for an issue that Thomann should have arranged for a didn't, but otherwise, I have been very pleased with it. It is of solid build, easy to handle, and plays really well with the exception of a somewhat flat high E, which is not uncommon on modern baritone. As far as the construction goes, there is no need to take my word, as Stephen Howard has reviewed the horn here.Of the B flat horns, which would you favour?
You talk about a high baffle, buzzy sound, so I assume you're talking about the mouthpieces that are matched to the instruments. I wonder whether this what would be thought of as the modern sound, and thus required in some areas of the industry. I also wonder if, as you might be intimating, a different mouthpiece and style of playing is possible on the low A's that would bring them more in to line with the B flats.
I completely agree with you that the matching of high baffle mouthpiece to a low A baritone seems to be a fashion and possibly even requirement, although this would be something to ask a professional about. It also works great in many contexts, as for instance Amy Winehouse. No doubt that lower baffle, bigger chamber mouthpieces and technique can bring out a much warmer sound in a low A horn, and some clips above demonstrate this. Whether a blind test would shown a difference to an equivalent low Bb sax, is something I don't know but it is different body tubes.
BTW, best of luck finding a horn that is right for you!