Well, to have this happen, wouldn't you need the Iran-Iraq War to be butterflied? In 1984 and 1985, both years you have chosen, Iran was at war with Iraq. Why would they start a war against Saudi Arabia, when they already have one. While I understand that OTL in the 2000's the United States sustained two major wars, but modern Day America is a very different story from the recently established Islamic government in Iran. Is Iran powerful? I would say so, but not that powerful.
Maybe Saudi Arabia could choose to go to war with Iran?
There’s a relatively straightforward way of doing this: Iraq loses the Iran-Iraq War and the Iranians take Baghdad. For a POD, if one of the Islamic Dawa Party’s efforts to kill Saddam bears fruit at a critical moment and the state falls into chaos, it could happen. Basrah falls, the Kurdish revolt goes into full swing, etc. The Saudis regard all of this as an existential threat and intervene in force in Iraq to create a buffer zone. There’s your war.