Monica,
Brady is correct regarding assumptions.
I’ll assume since you didn’t say running a new vent tube through through the ceiling would be outside of a wall in the room above, we are dealing with a single story home. The other thing is that the wall most likely isn’t load bearing due to the duct cutting through the plates.
More assumptions.
When you current ducting gets above the ceiling joists, it will probably return to a round shape. I just don’t expect a rectangular vent going out the roof:) You would connect round to round.
If possible, I would rather abandon the in-wall ducting, thus removing it from the system. If you don’t the exhaust fumes will be pushing both ways. I expect there is a technical reason not to tie-in midway, it just seems hacky to me and much more involved.
Your handyman was correct in backing off. Fabricating a flange out of sheet metal and connecting it to the current duct isn’t something something done easily if you don’t have the gear and don’t commonly do this type of work. Connecting two round ducts should be a piece of cake for your guy. Just emphasize that you want it installed properly, screwed together, then taped.
Another reason. MONEY.
If you can purchase off the shelf parts and assemble them, you will save money. Possibly lots of it.
Possible issue.
When the fur down was built, they may have placed a support board right where you need to go through. We don’t know yet. This is where I would bring out the inspection camera, drill a hole, and take a look around inside. You would also visit the attic and consider any blockers up there.
So, even if the attic is clear, there isn’t a joist in the way, the fur down could cause grief. In such as case this isn’t a blocker, just a bit of additional work to clear it. The dry wall weight would transfer down to the top of the cabinet. You would want to verify that the vent cabinet was tied into the surrounding cabinet very well, four screws, along with the verifying the nailers where used on both the top and bottom(those little long pieces of wood that go across next to the wall). Screws are only ten cents(not black drywall screws). BYW, I really can’t tell much about the cabinet construction or installation from the photos. Maybe none of this matters. Your crown looks nice.
Feel free to take picture or two in the attic of the duct work. We in the peanut gallery would be more than happy to provide you with more useless opinions.
We work with what we have.