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Two 4 foot doors? You do have a problem… but I have the solution. In fact, three possible solutions!
One option would be to mount four pairs of 2-foot bifolding doors.
Terminologically speaking, this means a total of eight one foot doors, hinged in
pairs. Because the "hinge" side of bifolding doors consists of a
floor-mounted pivot and a top-mounted track, you can install multiple 4 foot
tracks side by side with no need for a vertical wood support at either end. The
center door pairs would hinge in the middle of the 8 foot frame, giving the
appearance of two separate four foot closets when open.
If you really want the total 8 foot opening to be absolutely obstruction free (except for the thickness of the doors on either side of the frame), use bifolding hardware with four standard 2' wide doors. You can purchase a separate bifolding hardware kit, which includes hinges, track, and all associated hardware. Hollow-core doors would be the best choice, since the weight will be more easily manageable by standard bifolding hardware.
If you have a thing for heavy solid doors, mirrored doors or doors with glass panels you might find that the weight will overload the bifolding track/pivot mechanism. No way to know until you try it, though. Then, you would need to use butt hinges… either standard door hinges or special low-clearance hinges that require no mortising… to install the doors to the frame instead of using the bifolding track/pivot method. Obviously, this is a more labor and skill-intensive job, so trying the bifolding method first might be the way to go. The hardware is not that expensive. You could still continue to use the top track to guide the "leading" door of each pair so it does not swing out from the frame, keeping the bifolding function but with additional strength.
I can give you a number of options... choose the one that best suits your needs and abilities.
One would be to use solid doors instead of hollow doors. 6-panel moulded doors are available with a solid core allowing you to cut a little more from each edge without having the doors weaken. Just be sure to cut the same amount from all 4 vertical edges so the doors look balanced. Most prehung bifold door "sets" come with hollow doors, so you will have to order raw solid doors and purchase the bifold hardware separately.
Another option would be to use three doors instead of two... you would have to use standard hinges on the "outside" door since the standard bifold hinges have a support tab that is unattractive on the outside of the door. Then you need to do less trimming per door edge.
In your letter, you mentioned that the doors "bowed" after trimming. This is because you cut off most of the supporting wood along the edges. This wood can be replaced by cutting and then installing a wood strip along the length of the door to reinforce the edge. The new strip is simply glued in place and clamped till dry... usually 24 hours depending on your choice of adhesive. If you want to add a few nails or screws, do it from the back of the door so they won't show.