Can a vent hood designed for 12“ deep cabinets be installed under IKEA's 15”-deep cabinets?

Question

We're redoing our teeny-tiny condo kitchen (8 feet square), and one way we're saving space is with smaller appliances - 18" wide dishwasher, and 24" wide fridge and range. For the 24" range, we need a 24" wide vent hood, preferably an under-cabinet type¹.

Most places sell 24" wide vent hoods as a standard, stock item², so that's not the issue. The problem is, we're getting IKEA cabinets, and in their new(ish) SEKTION line, the wall cabinets are 15" deep instead of the 12" that everyone else does. IKEA does sell vent hoods to fit their deeper cabinets, but they're all 30" wide, which just will not fit, no matter how I play around with their kitchen designer program³.

So, I come to my question: can we stick an under-cabinet vent hood designed for a standard 12" deep cabinet under a 15" deep cabinet? And if yes, how? Would a 2×4 screwed to the wall, underside covered with metal flashing, suffice? Has anyone already done this? If yes, do you have pictures?

_{¹ Yes, you lose space inside the cabinet for the vent, but there's still room for things like baking sheets and cutting boards. Did I mention this kitchen is 8 feet square?
² I really don't understand this: 24" wide ranges are totally a special-order item, as in, for the options we wanted (electric, smooth top, and white) we had a selection of exactly... one. The vent hood is supposed to be at least as wide as the range. So why are 24" vent hoods standard? Who buys them? I don't get it.
³Which is awesome, but don't even try running it in memory-leaky Firefox.}

Answer 1

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.)