Hang the hood fan from the ceiling and just make sure the chiminey part is finished on all four sides and you might have to have the back on the hood finished on the back. The hood fan in this pic was actually one that was suppsed to wall mounted bit looked pretty good on the back and we just hung it with bollts into the ceiling. It was vented out the side so that is why we had a different chimney.

I agree with divadeva. More lights. If you can add pot lights do it. If they're already there add task lighting and up the wattage on the bulbs on the pot lights (replace with LED and you can make them brighter because the wattage on LED is lower for brighter light). If you have all of that add decorative lighting. If ventilation is an issue find a way to move the air around or add air filtration. Maybe the HVAC is deficient. Maybe you can add a HEPA filter instead of the standard one that comes with the unit. Call an HVAC specialist to see if there is a way to boost air flow in the room.

My go to hood is Vent-a-Hood for all of my high end kitchens. They are quiet, highly efficient, and different technology than any that you suggested above as far as the filtering.

I had purchased hafele hob 10 months back... I got it serviced 6 times... Now i requested for replacement with new one... Still they have not attended my request...