This is not the ideal solution and would slow down the loot a bit, but I used to go to a PuG raid where the raid leader had a set of dice in their inventory. They would ask who wanted the item, then roll the dice for those people and announce it in raid chat. Usually they would drag the people into their group so that they would see what the rolls were for themselves. Then hand the items out based on those rolls. If it was tie, then he would reroll.
For example, for the Wing 2 recipe - 4 soldiers want it.
Drag them into your group.
Type in raid chat: rolling for solider A - you roll the dice and get 4 - Type in raid chat: Soldier A got 4
Type in raid chat: rolling for soldier B - you roll the dice and get 3 - Type in raid chat: Soldier B got 3
Type in raid chat: rolling for soldier C - you roll the dice and get 4 - Type in raid chat: Soldier C got 4
Type in raid chat: rolling for soldier D - you roll the dice and get 2 - Type in raid chat: Soldier D got 2
Type in raid chat: Soldier A and C are tied, rerolling for A
and you get a 2, Type in raid chat: Soldier A got 2
Type in raid chat: Rerolling for C and you get a 3... Type in raid chat: Soldier C got 3, so Soldier C wins recipe
Not the most elegant solution to your situation, but avoids opening the box for free-for-all rolls.
Dice can be purchased from an NPC in the tradepost of your guild city.