I'm in the same position. My appliance guy suggested building out a plywood frame behind it. Then putting some kind of stainless over the wood. I'm envisioning the frame similar to what schicksal built to support her hood (but only along the back wall) about half way down the linked thread.

Here is a link that might be useful: hood support half way down thread

Thanks cal_quail. I was sleep deprived and couldn't make sense of schicksal's set up yesterday night. It makes better sense in daylight (don't most things??)
I also saw this thread where robj describes a stainless steel filler strip he put in to bring his 12" range hood flush with the 15" deep cabinet above. I am going to ask GC if he knows a local steel metal place that can make one for us. If not, I will ask robj's online supplier.

Here is a link that might be useful: robj's filler strip details

Thanks. That sounds awesome. If it's a known solution that worked, I'd rather just deal with them, as long as lead time isn't too long. I'm going to confirm measurements with parties involved, and hit them up. Again, thanks!