What is this new approach you two would like to try and impose upon them as outsiders?
From the Jordan River in the Land of Milk and Honey, To The Greek Mediterranean Sea?
Outside influence of bellicose Israeli enemies, such as Iranian Hezbollah, Houti's, and Hamas have copies of the keys to peace. They are reluctant to put them in the lock, let alone unlock it.
Are Sunni's and Shiites in agreement on ALL ?
The Golden Dome on the Temple Mount is a Colonization of an ancient BC 3,000 Jewish Holy Site; ( The Rock Abraham was about to sacrifice his son Isaac upon.) by the circa AD 700 arrival of the current Actual Colonists of the physical site, so that their Prophet may ascend from the same rock. (Descendants of Isaac's bro Ishmael). None of it is so simple. Many Revisionist Historians.
They call the wind the Mountain Moriah.
https://en.wikipedia.org/wiki/Foundation_Stone "The Noble Rock" Petra, Peter
The two of 'em have been trading eyes and teeth ever since,
and may make the whole world blind.
Then, Lop into the mix, the Christian holy sites... Nazareth, Bethlehem,
and yes, the site of the Rock of Abraham is the same site, that Jewish Jesus as a 12 year old, was found by his parents.
Sometimes referred to as "The Disputation of The Doctors" in art depictions.
https://www.wga.hu/html_m/d/duccio/maesta/predel_f/pre_f_7.html (13th century painting)
https://en.wikipedia.org/wiki/Moriah
https://www.youtube.com/watch?v=ByqYEzugleE "They Call The Wind Moriah"
https://en.wikipedia.org/wiki/Well_of_Souls
https://en.wikipedia.org/wiki/Holy_of_Holies
https://en.wikipedia.org/wiki/Axis_mundi
https://en.wikipedia.org/wiki/Shekhinah