I wouldn't expect an MDX (or a CRV for that matter) to be much more than meh on any tire.
I've only run A/T tires on the Jeep & Truck - not sure that's what you want(?) Always seemed to me that max traction trumps road manners in this type of vehicle, but that's probably just me.
It looks like you can upsize the MDX to a 265/60-18 to get a decent selection of a/t tires, but I certainly wouldn't expect them to
improve road handling and such over an all-season type tire.
It looks like you can get the Mich LTX M/S2 to fit, and that's probably what I'd pick.