Personally, I'm not that much optimistic about the Saudis, remember that prior to the war on Syria and in the first years of it, the Saudis were playing nicer than the Qataris, leading from behind they called it, unless they do something tangible I will remain skeptical. Their media remains very hostile against Syria and Iran.
Syria was stabilizing the Arab relations with Iran after the Iraq-Iran war until 2011.