I believe the easiest and best way to run a vent is through the eve fascia or soffit. I have two that run above the ceiling right out to the eve with a standard flapper and hood. Never caused a problem and worked for 40 years. The key is to run flexible vent from the hole in the ceiling for the new vent fan and push it out to the eve fascia. Cut a hole in the eve and find the vent pipe, connect and attach the flapper assembly to the vent pipe, then push it back into the hole. Wire the fan and done. Personally, I would insulate the vent pipe so you do not have a problem with condensation on the outside of the pipe in certain seasons.

You may run into insulation, which will require you to go into the attic and run the vent on top of the insulation or remove it to place the vent on the ceiling drywall and reinstall the insulation after done.

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Gary
SWCA 2515