outswinging mirrored closet door
Why not just fabricate your own?
Mount solid flush doors in a frame and have mirrors mounted on their face.
As long as you compensate for the weight of the mirrors in the hinge size a setup, you should be fine.
The push hardware can be gotten at most online door hardware retailers.
Woodworkers Hardware, Lee Valley Hardware, Seven Corners Hardware, Van Dyke Restorers, etc.
Who's cleaning the finger prints off the doors?
"They that can give up essential liberty to obtain a little temporary safety deserve neither liberty nor safety."
B. Franklin 1759