Bingo. you win the prize. that is it right there. that is the only problem i see with it. It's like going to Dynamis-tav and the first 18 get to go, sorry rest of you have to sit out. Our LS still has 18+ members go to dynamis when they all show up.
So split into two groups, and when one group gets something someone in the other needs, that person drops and joins the other group to lot on the item.

It's not that hard.

(and really- I can't remember the last time I had dynamis with more than 18 people)