Although I'm sure you've figured this out already I'm going to answer anyone else who might have this same question.
Keys are ra/ex so you can only hold one of a specific key at a time. Although you can hold 2 different keys, so you could hold one to Ordelle's cave and one to "The Maze," but not two keys for Ordelle's cave. Anyway basically to do this quest you must get a key, find/open the chest, get to jeuno, get back, get another key, open another chest... rinse repeat until you have all 4 pieces all within your RSE window.
I gotta say, the RSE does have decent stats for their level to hold up what they can in combat. The feet armor is awesome for DDs at their level. I've been wearing it since 29 and I'm 34 now. It's bad-*** (: