Specifically the efreeti boots & evolving items: I gather from reading the forums they only drop from the stratos mission: fight fire. Is that true or can they also drop from nameds, basepop or other chests like smoke trials?
When killing the final 4 make sure they don't die by a dot while they are stunned, or they will drop no loot, and fade off like they were killed by an NPC. Also , the final four are rootable and will not dispell themselves if not damaged. So, you can root 3 while damaging the one , and waiting through it's stunned phases.
Also make sure that not only is your task timer up, but your "loot lockout" in the DZ window. We had no idea that was even a thing, til a friend of ours pointed it out. We had been doing the task the moment the task timer was cleared. >.<