Without knowing much of Middle East dynamics I tend to like Dr. Codevilla’s analysis, in particular because by trying to engineer a result you often end up with unintended consequences, even in best case scenarios. Look at what we do with children: we want them to go in one direction and if we only push them a little too hard or a little soft, they spin out of control. Societies and states I am afraid are even more so, and the recent history of direct or indirect intervention in Afghanistan, Iraq, Egypt, Libya and Syria seem to prove the point.
Having said that I believe that two constraints are better than one. The parent at home is better off with his child if he is on the same page with the teacher at school. (The analogy is over simplistic, but it is an illustration).
So it is very absurd to try to engage both Israel and China in a confidential dialogue over Iran? The Chinese are worried about instabilities in the region and are eager to do anything that could guarantee the safety for the passage of their One Belt One Road. They are rational, maybe too rational for the crazy Middle East, but being rational are also extremely cautious with something they do not understand. Perhaps they could help in “stroking” Iran to normality, and as extra value US-China collaboration on a sensitive issue (the Middle East) could be a bonus. Israel, perhaps could be more comforted in having China in the picture. With the Chinese the Israeli are growing a good collaboration on many issues.
As for the players in the region, there is hardly anybody worth trusting, so mistrust them all equally, and equally manage them, with some extra support. At the end of the day, the Chinese need peace in the region for their railways, not the Americans, so this is a card Washington could play well, and the Chinese I guess would be willing to play along.