@Alexis,
A little old fashioned System & Process analysis of the Gulf.
As I look at the map we have 3 major arab communities on the Arabian peninsula, Northern Sunni, Southern Sunni and Eastern Shia. I am leaving the mix of Lebanon to the West out of this. The Northern Sunni are a minority under the rule of Shia in Iraq and Syria (Alawite schismatics). The Southern Sunni are empowered in Yemen, Oman and the Gulf. In the KSA they are ruled by the House of Saud who are I believe actually from the North and imposed upon the natives of the Hejaz and Nejd. The Eastern Shia Arabs are empowered in Iraq (for now) and under Sunni rule in the Eastern Province of KSA. This seems to be part of the engine of perpetual grievance. It is the result of the Sykes-Picot agreement of 1916.

It is not worth our time to postulate on grand rearrangements to produce more stable or pleasing arrangements. If such opportunities happen then fine but what we need to do is deal with the world as it is. The ability of KSA and Iran to play the US off between them is a good perception on your part. If new regimes took power in these countries they would still participate in a regional balancing system, with Iraq eventually being a player again. The current instability of Pakistan means that there is not a 5th power of comparable size able to participate in the regional balance for the Gulf. That decreases stability since a four power system lacks the freedom for members to switch alliances as frequently. As you pull back from the Gulf and include Turkey, Israel and India in the regional mix you do have enough comparable powers to provide alliance opportunities that increase stability.

If the virus of democracy that the US has introduced eventually produces regimes that are willing to ally with all parties, meaning with Israel, then a stable system could take root. Anything the US can do to encourage those changes, especially in KSA and Iran would be a step forward.