Is it viable to vent a range hood back into the kitchen?
Here's what I did in a previous kitchen makeover.  The original microwave (part of the range, not separate) vented into the wall, down to the basement, then to the outside.  For the new microwave I brought the vent up through the cabinet above the microwave, then ran it along the top of the cabinets to the outside wall (left in this picture).  This was hidden once the crown molding was installed.

Here's a close up view of the cabinet and duct work.

EDIT1 - Added picture below
Boxing in the refrigerator with a shallow cabinet over the refrig.