If you threw out the key after mission for rank 4 you can get it again, the NM will drop it if you do not have it in your posession - mog house or on you. So there is no need to be in a party that is trying to get rank 4. I solo the NM and got 6 keys, kept 1. I also tried to kill it again and I got 0 keys. Dropped the key I had, and wait for it to spawn again, and guess what - 6 more keys.
When you enter lower delfkfutt's, take a left at the first intersection and follow the right side of the wall past the stairwell and into a corridor. There will be a cermet door on the right, trade your key to it and it will allow you to enter (don't worry, the key remains in your inventory.) Go through the corridor until you enter a large room, take the first corridor on the left.
You will approach a long stairwell, but targetting the ??? at the bottom will automatically transfer you to the elevator on the tenth floor of upper delkfutt's.
IMPORTANT: You will enter the zone right ontop of polyphiron (or whatever his name is) and a room full of gigas. Since sneak/invis will not carry over a zone, you shouldn't use this shortcut unless nothing, including the NM will aggro you. There are roughly 8 other gigas who link fast.
Not sure if you can use it for the chest, as it is not named "Delkfutt Treasure Key", but anyway it can be used to do shortcut through this mission again if say you were to switch nations. I personally switched allegiances from Bastok to windurst after attaining rank 4 in bastok. Because I kept the key, I did not have to climb all the way to floor 10, but could just take the locked door on floor 1 and walk into the basement where you actually rescue the ambasadors.
If you'd ever like to decide you'd like to switch nations, it's an incredible idea to keep this key. Rather than doing this whole mission over for the other nations.
There was a chest on one of the levels by the stairs down. I asume the key will open the chests just as any other "named" key will open chests found in said "named" area.