The less-violent solution is the sensible one in this case.
Israel should take control over ALL holy sites in their nation. Making it very clear that the religions of the world who honor these sites will have liberal access to them.
They may use the sites freely, but they are the property of the nation of Israel. NO other nation or religion can claim ownership of ANY of them.
And that they are allowed use of these sites ONLY so long as they behave themselves. This means:
NO violence
NO advocacy of violence
NO fights between religions
NO changes to holy sites without Israeli permission
This also gives the Israelis tremendous leverage. Say for example, if the Wahabbis who run al-Asqa misbehave, then Israel can turn over management of al-Asqa to the Sufis.
Even the threat of doing this would scare the Wahabbis silly.
But the bottom line must be to let everyone know that ALL HOLY SITES IN ISRAEL ARE OWNED BY ISRAEL. NO ONE ELSE MAY CLAIM OWNERSHIP OVER ANY HOLY SITE.
As a Christian, I agree. Every nation must exercise complete sovereignty within its own borders, or else it isn't a nation.