Paul wrote:

I currently have an over-the-range microwave with the built in "range hood"
that just basically sucks the smoke up and blows it back out over your head.
Very noisy and relatively useless, IMHO. I have an old unused chimney
right behind the stove that would be very convenient to run a duct to. Is
there an OTR Microwave with a ducted hood out there? Or another way to put
some kind of "low profile" ducted hood under a regular OTR microwave?

I'm not sure you want to put a stove-vent into a normal chimney.
If it's really unused, it won't be much of a fire hazard, but the eventual
grease build up will feed an interesting array of flora and fauna.