Hi everyone.
Apologies in advance for a very long post.
TLDR: need options for covering an entryway to a study room.
Details:
As soon as we enter our home from the front door, on our right we have an entryway to a small study. It doesnt have a door. It is 1300mm wide. I have my office set up there and would like the option for some privacy when I'm in the zone. For reference, I have attached a picture of the entry as seen from inside the study.

*Overall width of wall - 2400mm (in red)
*Width of opening - 1300mm (in red)
*Barndoor hardware rail length - 2000mm (in blue)
*Possible location of a header board (green highlight)
I have been thinking of adding a barndoor to the space.
The concerns with that are:
1. The barndoor will meet at the perpendicular wall when closing.
2. Barndoor hanging hardware needs a header board. With the space i have, the header board will be partially hanging on the right half as there is no wall to attach it to. That's 1300mm of header board hang without support until it hits the perpendicular wall. Is this a dealbreaker?
3. What would be a sturdy and aesthetic way to attach the header board to the perpendicular wall?
4. What thickness should the header board be? Can I glue two 140x19 merbau deck boards to make it as the header board that can resist the sagging across the unsupported 1300mm span?
5. There is an evaporative cooling vent right in the middle of the unsupported span and I am not sure if there is a beam on either side of the vent that can provide a possible hanging support to the header board. Even if there is one, it will be too close to any of the wall that it will be inconsequential anyways.
6. The door will need to be at least 1400mm wide to cover the 1300mm opening.
7. There will be an opening at the top of the door because the door and hardware can't be ceiling hight. I am wondering if that will look weird.
8. I am thinking of building a hollow core door, 1400mm wide. Frame made with 25mm x 25mm pine and covered with 3-4mm painted mdf or ply on both sides.
9. I already have a barndoor hardware but that unfortunately has a 2000mm wide rail. Can i hang a 1400mm wide door on 2000mm long rail so that it moves across 2400mm range of motion. The only way that seems to be achievable is that the hangers are attached to the door at least 250mm inwards from the edge. I know that is not a standard practice but is there any issue in doing this?
In essence, my main botherations are covered in points 2 and 9. Is barndoor really an option for me at all?
I know Pocket door is not an option because the wall that will envelop the pocket door is an external wall. I don't want to do a major renovation for adding a pocket door.
A bifold door will have the same issue of a partially unsupported length.
I would love to know what the experienced people from this forum think of my plan and the issues.
Varun