Reply by oluf

I wouldent cut the joist at all.I would make a plywood box (flue) that straddles the joist and the roof rafter. attach it to the joist to hold it in place. Caulk the seames and use it for the flue connector . cut a hole in the roof and install a vent cap. Attach the vent to the plywood flue box, Your hole in the celing can be 16” square.

-- Nils, So. Central MI. Wood is honest.Take the effort to understand what it has to tell you before you try to change it.