The installer working with the duct situation came up with a great plan.
New location for the duct.
The duct would run up the wall behind the fridge, along the top of the cabinets, between the joists and into the existing hole. This would eliminate cutting the joists, losing headroom in the basement and having the duct in a cold space. The box on the wall would be eliminated and placement of the window does not have to be exact and providing more room for the casing.
Only one outlet would have to be relocated, so I think that this looks like a pretty good option. We will see once I pick up the window tomorrow.