410.16(A) says: The volume extends vertically to the closet ceiling parallel to the walls at a horizontal distance of 300mm (12 in.) or the width of the shelf, whichever is greater.The storage zone only goes to 6' high or the height of the rod, whichever is higher, so if you can get the surface of the light 12" above that you are compliant. If you have a 7.5' ceiling, you should be able to fit just about any LED fixture in the ceiling. Recessed cuts the clearance requirement in half to 6" if things are tight. Flat LED strip lights intended for under the cabinet work nicely above the door on the header. I wish part (2) also had the word LED instead of only fluorescent.
Only if it meets the exception in the NEC section quoted in the OP. Otherwise, with a 36" wide closet, any location of non-zero size within the room is within 6" of the storage space shown in post #5, and so can not comply with any of (D)(1) through (4) in the OP.You could even install one in the wall above the door.
That website search is not limited to the correct specification for the situation in the OP. The very first item's spec sheet just says "Suitable for use in clothes closets when installed in accordance with the NEC 410.16 spacing requirements." For the exception, sounds like the necessary specification is "Closet-Rated Certified" or some language saying listed for use within the storage space.Here is one site (not the only one) that has multiple fixtures identified for use in cloth closets.