Now that's something rather unique! BDM make excellent bats, they tend to taper the width of their bats slightly from front to back, so width at front can be around 107mm and back could be 103mm. Clever way to pack the wood in the central area/make a bat appear to have more volume than it actually does.
Do let us know how it turns out!
In terms of higher middled bats, Amplus, GT, one of the Charlie French shapes and one of the Chase shapes too. The old Kookaburra ranges from 2013 all had high middled too from memory!
Always find higher middled bats give excellent coverage and pick up, while lower middled bats tend to keep the ball hit!