I am replacing my over-the-range microwave with a new one, and I would love to vent it to the outside. However, my range is on an interior wall. There are rooms on three sides of the kitchen, and a second floor above it. The one wall of the kitchen that is an exterior wall is opposite the wall that the range is on.

I was considering running ductwork up through the cabinet above the microwave, then make a 90-degree turn and running it across the finished ceiling to the exterior wall where it would vent to the outside. I would then hide the ductwork running across the ceiling with a wood box cover. The vent would exit the kitchen above the only window. The ceiling is 8' so there is room to run the ductwork. I am fairly sure that the joists run the wrong direction to run it through the ceiling.

Is this a feasible option?