That looks like a PITA!
How often are you in the room? At first glance, I would consider air sealing the doorway itself and just having the mechanical room belong to the exterior of the home envelope, similar to a garage. You may need to seal around your baseboards as well (pull them off and run caulking around the seam between the drywall and the foundation).
Weatherstripping, and even possibly run a door jam along the bottom so that you can more easily seal all 4 sides of the door hole. Pressing up against a seal is more effective than a skirt that is attached to the door.