I have a half wall between my kitchen and living room. The half wall is raised up for the 44" tall breakfast bar thats going in. Puting a ceiling vent or range hood is not really an option at this point. Would it be possible to place a vent in the half wall right behind the stove, have the blower motor in the basement and then vent it to the outside from there? The stove will be a slide in so there wont be a back to it.
I would question the common sense decision of putting the stove under the breakfast bar location. Passing food over the top of a working stove is asking for trouble.
As for the venting, this setup would be a good spot for a down draft stove. What you are planning would require a filter system to catch the grease and cooking oils before it got into the ductwork and fan blades.
The fan motor would need to be strong enough for the distance and route of the ductwork. The choices you picked are only guesses as this is an off the cuff design.