It seems to me that if they find a few pounds or a serious amount of coins or treasure, they would bring up enough to get attention. That sacrificial amount could be turned over to the state. Enough to garner attention but more, a whole lot more, would be on the way once the recovery permit is issued. If the dollar amount of treasure is what they say it is, a pound or two won't make a big difference.
But you are essentially splitting hairs here with how that will unfold. The bigger picture is whether they find treasure and how much. Kyle will take care of the permit as he has in the past. The state gets their share, Seafarer gets their share, shareholders make money - win, win, win.