Designing Kitchens and Bathrooms - Downdraft vent for cooktop

I want to replace my downdraft cooktop with one that doesn't have the downdraft built-in. I have granite countertops and my cooktop abuts an eating counter that is raised 6 inches above the cooktop. The top of the eating counter has a lip that sticks out about 3/4 of an inch. I don't have enough room in depth to put a pop-up vent behind my cooktop because the lip gets in the way. There also isn't enough room on either side of the cooktop for the vent. Does anyone know of a way I can put a vent into the raised portion (6 inches) at the back of the cooktop and install some kind of grillwork so air could flow into the vent when it is turned on? The raised "6 inch backsplash" is granite, but I could have a cut out made for the grill. Any help would be appreciated. I really hate the cooktop options with downdrafts built-in.
Thanks!!!

Tough question. I don't know of anything, but I'll bet if you try a kitchen specialy shop, they will. They get your type of problem all the time.