The term "haunched" is misleading. For mechanical ducts through a beam web, it is usual to provide openings through the web reinforced with angles top and bottom such that you have a panel of a Virendiel Truss. For a single round duct, you might use a pipe section a little larger than the duct; the pipe section is welded to the web.
Calculate secondary moments at each end of the opening and combine with primary moments to determine if okay.
I thought you were providing an opening in the beam web to allow the passage of ducts, so I misinterpreted your question. I see now where you got the term "haunch" but it really is more of a recess than a haunch. Is it possible to use a shallower beam throughout the length and avoid this awkward detail? The beam will be much heavier, but it is probably more economical than this.
It could be built as shown but I think it might be simpler to splice two beams together, adding plates as required to gain continuity of the bottom flange.
The items to check would be deflection of the odd shaped beam and stresses at the transfer point.
I've shown a couple of alternatives below. For high shear and large copes as you have here, my preference is option one with the vertical stiffener. I've attached a good paper discussing the failure modes that you'd check if you were to do this without stiffeners. I feel that's pretty relevant as the point of your stiffeners is to effectively deal with the same issues.
