What would you like to see in it? 
The problem that typically arises when building the table for the unique chests is that we can't just give Hakkon weapons to someone who has been playing for 4 or 5 weeks. We usually attempt to split it based on what you're loot score is at but as you can guess it always leaves people that are just under the next jump very upset (1 item could be the difference between a Hakkon weapon and a level 18 epic for example). The other option we have is to just pick some of the top accessories and build a big chest of those and set them to only drop if you don't already have them.
Lots of options but I suspect no matter which way we go some people won't be happy with it - such is the way of the chest 
At least you are able to add that sort of logic to the chests. I remember an ME3MP Biower guy posting that the purchasable packs could only be purely random, which of course means the potential of never getting an upgrade.
Would it be possible to make a separate loot score formula for chests you really want people to get an upgrade from? Just something that kicks it up a notch. You guys did already raise the loot score cap, didn't you? Is it high enough for people over nine thousand power level?
Of course, you could always do what ME3MP did on occasion and give us a unique banner, icon or title. Not this time, I suppose, since it already says "Chest."
Speaking of which, we need a better way to find the ones we have unlocked. I am sure you have noticed searching the challenge stars is a little silly.
The accessories pool idea is a good one. I play all my characters so I would be happy with a weapon from any category, but I would imagine some people don't.
I don't know if you could rank them: "If a player has X and Y, award one of these."
I can't recall exactly how you changed looted armors recently, I know I read something about it, but giving an armor for a new character or an upgraded armor for an unlocked character could work. It'd just be tricky to lock out sidegrades.