The export of dollars has to do with the fact that if every nation runs a trade surplus then there must be an escape hatch or deficit black hole that soaks up the deficits. That black hole is the US. Things would be better if we had an international clearing union but that is a pipe dream today.
I'm not sure I see a practical way out of the current system that returns us to a more free market system. Instead we see carbon credits promoted, perhaps as a part of a SDR like system.
Where the petrodollar required somewhat incoherent rationales for war, a supranational carbon credit regime would offer somewhat more self-coherent rationales.
It isn't difficult to imagine how it might play out.
"Nation X's refusal to honestly participate in the carbon credit system is a crime against the Earth. Sanctions have been insufficient. The global coalition must act militarily to protect the Earth from..."
Regardless, I'm not sure there is a practical way to get the US back on track to where markets are more free and investment in domestic industry isn't distorted. A 25% tax credit or outright government funded or perhaps an initially nationalized industry? The difference is only in degree.