I have a couple of thoughts and questions, how wide is the linen closet door and or opening? If you can go down one size on the door, for instance, if the linen closet door happens to be a 2/0 then you could replace it with a 1/8 door. Of course this depends on how wide your door casing is. If you have 2 1/4 inch casing then dropping the 2 inches in door size might not quite cover the rough framed door opening, however in this case you could rip a 2 x 6 down to 4 1/2 inches that is assuming you have half-inch sheetrock on both sides of the opening at which point you can place it at the inside corner and if necessary tape and mud the joint between the sheetrock and the 2x. Of course you can throw all of this out the window if your linen closet door opening is already very small. But this could be a solution to your problem. Keep us posted to let us know how things work out. Is always happy woodworking.