You can reorder the files by changing the date stamps on the files. The most recent date stamped files will appear closest to the bottom of the list. There are lots of programs that edit date stamps, including LOOT, which includes an option to re-date stamp your files.
http://www.gamesas.com/topic/1505791-quick-questions-quick-answers-thread-43/page-6#entry23745219
As it turns out, the solution was to import the mesh into Blender, re-make the UV map on my transparent objects so that adjacent faces were as contiguous as possible on the map and proportionately sized, then re-export the mesh and copy the NiTriShapeData into my object! After that, using flags 4333 in the NiAlphaProperty worked.
I probably changed something crucial in the mesh on the way, but I couldn't be sure what .