Instead of moving the single door, you can consider enlarging the frame to hold a double door and use the side furthest from the stairs to enter and exit. It's still going to be tight but you wouldn't be walking backwards up stairs to go in and out. The side in front of the stairs can be made inoperable although it might be handy to have a wider opening occasionally for moving furniture or large appliances. By having the door swing to the left, it wouldn't bang into the posts or block the path from the stairs.
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