I was thinking the other day. Why not do this, but to a rackmount chassis? With some good insulation, low noise squirrel fans, and put the exhaust ductings to face a room window?
This is a similar method to how we cool racks in commercial server rooms.
Raise the racks up from the sub-floor with a ventilated space below and force cool air into the space. The cool air then passes through the racks picking up the waste heat and is ejected from the top of the racks into the room. The indoor unit then draws the warmed air into the filters and the process starts all over again.

Been like this for donkey's years. It's called downflow configuration.