Create something similar to mechanics in the other games where you burn few items to get a higher level one. I will use Rocket League as the example.
Example from Rocket League
There are few rarities: common, uncommon, rare, very rare, import, exotic, black market.
You can burn 5 items of the same rarity to get a random item of the higher rarity.
Illuvium example
You burn 5 tier 1 stage 1 items and you get a random tier 1 stage 2 item.
You burn 5 tier 2 stage 3 items and you get a random tier 3 stage 1 item.
*numbers will have to be played around, but hopefully you get the point.
Rational
Cheapest accessory currently has the floor of 0.000037 ETH. With more packs opened, that floor would go down even more. At one point nobody in the world would have any need for that accessory and we could just burn it so it doesn't take up any space. But this way it's actually useful. You can continue playing the game with burning items and getting and loading new ones.
Possible problems
Numbers have to be played around. It possible it would devalue some of the higher rated accessories but I think if the numbers are set correctly it can work just fine.
Benefits to DAO
Use for lower level accessories grows. They aren't priceless anymore. You spend more time in the Illuvidex burning items and playing the game to load better accessories.