Re: 12 inch tall horizontal cabinets?
Hi dcmom and welcome!
IKEA does not make 12" high cabinets, they can be hacked/fabricated, but the main problem is that they don't make 12" high doors, so the only alternative is a 12" wide door hung horizontally. I've also hear that the 30" horizontal cabinets (available in 30" and 39" widths) do not exactly match the width of the 30" wall cabinets, nor would a 12" wide cabinet laid on its side, I don't think.
I'm not clear but are you replacing all the current wall cabinets when you take down these soffits? If so why not just use 39" high cabinets and boost them up an inch or so (a higher backsplash is usually good) and then add some trim at the top? This might be less work and less money too.
I've had clients with an unattractive exhaust vent just build a small 3-sided box to cover what's visible between the top of the cabinet and the ceiling.
Have you posted a copy of your plan here (we love plans!)
Best of luck with your project,