Perhaps...would it be possible for the Palestinians in Jordan to pull off a coup if there are more of them (booted out of Syria)? Then you could have Jordan as the evil extremist country...maybe.
I think the Royalists in Jordan would probably still win the civil war, since I think that Iraq and certainly Israel don't want Jordan to become a puppet of the Syrians.
The loss in Jordan, plus a more Soviet-oriented Syria, could end up meaning that the Syrians become even more involved in Palestinian affairs, and end up de facto controlling the PLO.
When the Syrians are defeated in the '73 war Jadid's regime loses all popular support. The moderate wing of the Baath party has been eliminated in the wake of the failed '70 coup, so there is no Baathist alternative, and when Jadid is assassinated in '74 in what is seen as an only partially successful coup attempt, there is a popular uprising. Out of this chaos I don't know what kind of government emerges.
With Syria in chaos over the fall of Jadid's regime, Lebanon faces the prospect of falling to Palestinian militants. The failed Jordanian militants, along with Palestinians who had been sponsored by the now-defunct Jadid regime, all flow into Lebanon, giving the Sunnis a key edge in the Civil War. After massive Lebanese Sunni-Palestinian gains, the Israelis decide that the PLO appears about to gain control of Lebanon, and after the assassination of Suleiman Frangieh by Palestinian militants, intervene in Lebanon. Middle Eastern politics starts occuring, ie I have no idea what happens after this.
Otherwise, I think you need to say Iraq, as you thought. This has run-on effects. If Saddam stays in power, and decides to invade Iran, the US isn't going to help him at all, since Iraq will be the extremist state in the region. Eventually this means that Iran is going to defeat Iraq, unless America intervenes.
With the example of Syria's ruler falling the wake of an unsuccessful war, combined with Egypt and Jordan making peace with Israel, Saddam might think much more carefully think about what he does. In addition the example of Syria's regime falling could make the Iranian opposition prematurely attempt to rise-up, thinking the time was ripe for revolution, with Syria in revolt and Lebanon about to fall to the PLO. The earlier revolution fails, and the Shah is able to hold onto power, so Saddam doesn't have a chance to go to war. He does get heavily involved in the Syrian civil war, and it takes up a lot of his desire for martial glory, while sparing Iraq the strain that the Iran-Iraq War caused.
Iraq's increasing modernization, and sponsorship of Syrian factions that Washington sees as the most "pro-Western," along with the Shah having to deal with a serious rebellion (making his regime appear a lot less stable) causes Iraq to be seen as a potential agent for American policy, a hedge against the possible loss of the Shah. American aid for the now Iraqi backed Baath Party in Syria (full of people acceptable to Baghdad), increases markedly after Reagan's election, along with American support for Iraq more generally.