Can a vent hood designed for 12" deep cabinets be installed under IKEA's 15"-deep cabinets?
Find a decent hvac fabricator and they can bend you a 24" x 3" sheet of stainless steel. 

The simplest way to make that work would be to put framing lumber against the back wall (2-2x4 upright for 3" width) and slap the steel against it. That has the advantage of being solid and offering an extra spot to attach the hood. 

Depending on your cabinetry, you might be able to vent through the back, which will give you more space in the overhead cabinet. (This might lead you to a 3-1/2" spacer to give a bit of room for the typical 10x3-1/4 duct.)