I have seen builds where people created sub enclosures as part of their walls. Your space may work for such an effort but I know very little about this.

Essentially you do as you said, but take it further and actually build a sub enclosure under the stairs. The opening to the room is where the driver goes. I have seen ported and sealed versions of these. The sub then takes no space in your room.

Others that know more about this can chime in.