A shallow vent is only slightly more effective at cooking plume capture and containment than a vent somewhere else. The hood should overlap the cooking zone sufficiently to capture the rising and expanding plumes. If the vent is low enough, perhaps it would adequately deal with rear burner/hob effluent.

I don't see a photo, and you didn't mention how deep the upper cabinets are and how high above the cooktop. Were you planning on exhausting the effluent through a duct in the cabinets, out the hood rear, or back into the room?

Stupid idea unless nothing is ever cooked in that kitchen. Even then, it would totally kill resale.

Kaseki— The cabinets are 13 inches deep and will be hung to code, which i believe is 28 inches above the range. We have a duct that vents outside. I am not sure why the picture did not post. I will try again.

That's a staged or photoshopped kitchen that will ne3ver get used. Those "hoods" are just this side of useless.

Look at the Vent-A-Hood TLH tilt out hood. This has the ability to he "closed" when not in use and look like it is a cabinet. When cooking you can pull out the bottom of the hood so it give you some capture of the cooking contaminants.

OP, thanks for clarifying. Unfortunately that cabinet style is at odds with the physics (fluid dynamics) of cooking plumes. A truly huge and noisy air flow rate would be needed to even partially collect more than a small portion of the potential cooking plumes.

Generally, one should evaluate residential hoods by the degree to which they deviate from commercial hoods, which are intended to efficiently and fully capture and contain cooking plumes. The first dozen or so pages of the reference below may add further enlightenment.

https://www.tagengineering.ca/wp-content/uploads/2015/02/KVSApplDesign_catalog.pdf