That's too 5-d chess for "the US" to pull off.

It is not a complicated strategy. It just requires a large group that cares about the petrodollar. The US has a ton of those people in high places in government and finance.

The US invented the petrodollar.

I find it more plausible that the US supports Israel because Israel has a lot of powerful supporters in the US who manipulate public opinion and government policy.

Israel has powerful supporters in the US because it is in the interests of capital to support Israel. The higher interests of capital do understand why the Middle East must be destabilized for their own gain. They are fully aware of and influence, for example, the invasion to control Iraq's oil fields and depose the government of Iraq that was acting too sovereign about it. Same for the Syrian oil fields seized and controlled by the US to this day. This is also why the US promotes the Saudis as an ally - they stabilize the petrodollar system. It is no coincidence that they also target an independent Yemem.

Powerful supporters are just the middlemen for capital, as are major media campaigns. It is not explanatory to say that powerful people support a country or policy. Of course they must do so, that is how every policy decision happens: the powerful people fall in line with the decisions of capital, decisions that may have been made decades ago but are now entrenched. Capital also leverages its close collaboration with the highest levels of the state. The White House is constantly consulting finance, economic advisors from finance, think tanks built to advance the interests of finance, etc (finance is the dominsnt wing of caoital in the US). And in the other direction, capital is constantly making threats and PR pushes.