How about this; bring the head of a Hamas leader, and the US will consider that proof of wanting asylum. I call that the 1 for 1 exchange.
Everyone knows where the Hamas leaders reside, which school their kids go to, which business they own etc. They all reside in palace size buildings in Qatar.
Israel and US can finish them in one drone strike. But they can't because of powerfull Qatar lobby in DC and the fact that Qatar is a Oil and LNG supplier. The US also has a base in Qatar.
In Gaza the only high value target or HVT is a Hamas commander and rest of them are all potential Hamas terror fodder.
Remember Palestinian people, Hamas, Al-Qaeda, Isis, Taliban are all sunni muslims who where funded heavily by Qatar. While Iran is Shia and the IRGC and Hezbollah shia fight against Sunni Isis in syria and occasionally fight against Taliban but because they all hate Israel and USA, they work with Hamas enemy of my enemy is my friend.