Trying to come up with a cost effective idea to install an extraction fan in a small kitchen (10' x 10'). The bottom side of the cabinet above the stove is 82" from the floor and is 12" deep.

Considered cutting the cabinet away above the stove so an extraction fan wouldn't block the window at all, but that puts it 48" above the cooking surface (would it still be effective at that distance?). Not to mention the controls would be hard to reach.

Also considered a low profile range hood that may only block 6" of the window . . . it doesn't seem like there will be a simple clean solution.