Designing Kitchens and Bathrooms - Re-routing Hood Fan Duct

My current hood fan is the standard 10" x 3 1/4" and ends up deep inside the eaves right up against the very corner of the end of the building. It is has no cover (other than the soffit and soffit vent) and I cannot get a cover/flap in there because it is so tight to the end. I tried modifying one and it failed miserably. Cold air pours in during the winter so badly that I'm stuffing insulation in both ends and don't use the hood fan at all.

It seems my only solution is to re-route it which can be easily done but what exactly do I do to block off the old duct that will be bypassed?

Damper, cover, etc., is a necessity for any vent. I have had to install some seemingly impossible vents on existing vents, over the years. If you must abandon the old vent, cover it with aluminum or similar to blend with the surroundings, after stuffing the opening with insulation.

Have you tried putting a flap or backflow preventer just above the hood? That may be an easier place to work. Where do you propose to reroute the vent? Once you disconnect the old vent from the hood, just leave it in the attic. You can stuff it with insulation, but once disconnected it can't dump cold air anywhere. If you have an opening at the soffit, then you will need to address that, by a new piece of soffit material, as I am not sure what your attempt to install a flapper on that end did to the original soffit.