Most closet doors don't affect the floor at all. Just have a carpenter "frame in" a doorframe (he'll screw the frame to the studs that create the opening for the alcove) and attach a door with hinges.

Here's a bifold door--note that there's nothing attached to the floor; see the doorframe as well.
http://www.diyshutters.com/images/gallery-bifold-6232-bedroom-800.jpg

Here are regular old-fashioned closet doors--note that there's nothing attached to the floor underneath.

http://www.doityourself.com/forum/attachments/closets-home-organization/7463d1357329955-closet-project-install-bi-fold-door-joining-2-closet-door-expanding-photo.jpg

Another example.
http://www.perfecthomeremodeling.com/images/Right%20side%20-%20after.JPG

My vote: find a carpenter or small construction company; get them to come make a proposal.

The rest of my place has closet doors that go from floor to ceiling. There is a 1.5" rail that attaches to the ceiling and then each set of doors has a bolt that goes to the floor. I would prefer to find those so it matches, but am having a hard time finding them. The door+rail is for an 8 foot ceiling.

I guess with as wide a space as you've got, that center support might be useful. Could you build a wall that comes out from the back?

But if it's just two doors that meet, and one of them has a bolt that goes down to keep the door from wobbling (sort of like this, only maybe it's more spring-loaded?) http://doorhardwareusa.com/admin/uploads/surface_bolt.jpg

then you can just leave that bolt off. If it bothers you that the two doors still shift a little without the bolt, you can use a latch that makes them snug to each other a bit more firmly.

Also, FYI--the "ball catch" can go on the TOP of the door, anchoring into the door frame instead of the floor.

I would say that if you think that closet is needed, why wouldn't some future buyer? And I'd also say that *you* are unlikely to want to eliminate it.

And I'd further say that this small hole in the floor might patch more easily than you think.

As for matching--you could do a plain flat door (drywall-type surface) and paint it to match the wall, instead of pretending that it's a real door. Then it's just sort of "a part of the wall that opens." You can even hang a picture on it!

I still say--get a carpenter or small-jobs construction person to come in and discuss options with you.

Here is a link that might be useful: door hardware site--ball catches.

I think you should take some advise of carpenter. Most of the closet doesn't cover huge space ,he will definitely adjust your closet in a space where you want.