Doors – What hinge is this

Before you get started carefully evaluate if you really really want to have a pair of doors that swing out 18" into the room. In many bedrooms this is likely to be a less than desirable thing to have. If you are having a hard time visualizing what this would be like then you should get some large cardboard boxes and make up a fake set of the doors and duct tape them in place for a few days. Then with normal usage of the room you can swing the fake doors open and shut to see if the 18" interference is a pain or not.

Do not try to install the door hardware right on the top of the drywall. You will indeed regret doing that sooner as opposed to later.

The really correct way to do this is to remove the banding drywall material. (This will likely be more work than first guess because there is highly likely to be metal corner pieces installed on each corner of the opening). You would also remove the banding drywall at the upper side of the opening along with any previous door track hardware. Then you would fit in new boards to make a proper jamb for the doors. These will want to 3/4" thickness and not the 0.5" thickness that you proposed. Proper door fitting will demand that there be a small gap between the jamb and the exposed stud faces. The gap is used to allow the adjustment of the jamb opening so that it is perfectly square and plumb. Tapered wood wedges in the opening help to wedge the frame one way or another.

After the jamb is in place the trim is installed across the gap to bridge over the space from the jamb out over the drywall.

You should also plan for installing door stop molding which gives an edge for the doors to close against.

Door Comparison

I've added a couple of pictures to my answer to show the advantage of bi-fold doors in terms of how they project out into the room less than full swing doors. First off you would want to use a pair of bi-fold doors per opening for optimum usage. The second point is that the pivot point for bi-fold doors can often be recesed into the opening which lessens the projection distance into the room. The latter comment would also apply to a single bi-fold door application as well.

I can appreciate the fact that bi-fold doors use up some of the opening width. For your most often used closets you may want to consider the possibility to widen the opening which of course is not a trivial project. But then what is the price of convenience.

Also closets with deep blind ends are indeed a pain to make use of. Often it can be advantageous to re-fit the closet pole in such closets so that they go across from the front to back of the space at the ends so it is easier to take hung garments in and out.

Plywood will not sag over time if you intend to use it for the door faces. I recommend birch plywood for not only its hardness but looks. However your hinges and what they are attached to are the big concern in this project. It looks like you've used a low grade pine to build the unit. This is a soft wood and a couple of cabinet hinges screwed into this are going to loosen quickly. Your best chance for longevity is to use a piano hinge so that you have a continuous hinge from top to bottom with 15 screws or more on each hinge. I highly recommend ordering a stainless steel or flat nickel piano hinge for this. What they have in stock at the box stores is of the "bright" variety and looks cheap to me.

I'd also recommend that you not attempt to build the door to be perfectly flush with the "lip" at the bottom. Leave yourself 1/4 of an inch gap. Units like these always sag at least to some degree and you wind up with the door scratching the "lip" and its going to look really bad with time.

Also take a look at ball catches to use either at the top or bottom of the doors to hold them in place once closed.