I must admit I don't understand why Israel would risk a wider war with Iran just to avoid having Hezbollah (or anyone else seen as an Iranian proxy) to use Syria "to become a forward operating base against the State of Israel." Doesn't Hezbollah already have that in Lebanon? The group's heartland is the Shia area that runs the length of Lebanon's border with Israel. Why would having a base in Syria make any difference when they already have a "forward operating base" in another neighboring country?
Maybe those questions have an answer. But I still think it's odd that the articles I read about Israel's stance towards Hezbollah in Syria don't even mention Lebanon, or note that Hezbollah already has a presence right on the border with Israel. That seems pretty relevant to me.
(Photo is a Hezbollah flag I photographed when I visited Lebanon in 2005)