you could argue to move the jewish population of Jerusalem to the East or West Coast of the US. There's ample room there and enough "native" jews already to feel at home. The historic connection of Jews and Muslims (and Christians BTW) to Jerusalem and the holy land as such is equally valuable unless you consider your religion to be more "right" then the others. I guess not many Jerusalimtes would object to the annexation if there would be real equality for the population of east and west jerusalem but as you know yourself, this is by far not the case. And Mekka and Medina really do not matter in this dicussion. Or would you give up the claim for every other jewish historical/religious sight (such as Josef's tomb etc.) if you get Jerusalem in exchange?
EU's Mogherini in Tehran to talk nuclear deal, regional issues (Reuters)
from the article: Netanyahu: Arabs and Jews alike benefit from unified Jerusalem