Need some advice on ducting a 48" vent hood. Appliance installers can't figure it out, my contractor is at a loss, and the guy that did my HVAC is just as confused.

My wife's dream kitchen involves a professional cook top (48"). We bought the cook top and the hood, and are currently down to studs in the kitchen. Along that back wall, is the range/ hood's destined location. We did this during planning because we were told the 48" hoods needed a large duct, and to place it directly on the exterior wall. Cabinets, windows, etc. were all designed around this hood. Now we're getting to the rough in, and we're planning the ducting. This is where everyone is lost:

There is a supplied 10" round transition that comes with the hood, that screws into the 8.5" x 8" opening on top of the hood. It says in the manual "Minimum Ceiling Height for REAR WALL EXHAUST with duct covers is 8' 4" when installing 30" above the range using 10" elbow". This is what is confusing. Has anyone had experience with a different transition? Like this one from vent-a-hood? It's too small for the 48" Monogram (needs a 10"), but wondering if I can have a fabricator make something that vents straight out like that.

I tried posting to HVAC Advice, got no response. I appreciate any valuable experience anyone has, as we're lost until we find a solution. Thanks for the help, it's really appreciated.

submitted by /u/Melloncollieocr
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