You don't create carbon out of thin air, it's from the fuel, so burning the same quantity of fuel will result in the same quantity of carbon, no matter how the engine works. Therefore a tax on fuel is a tax on carbon.

Ethanol blends get worse MPG, and entail additional carbon emissions in creation. They do not reduce carbon emissions.

What is the point of the link?

Unless you play in the nuclear physics, Carbon in is Carbon out. Carbon in fuel is Carbon out of the engine.

Incomplete combustion is a big component of emissions, and it's exactly what you're saying doesn't exist

Yes but since incomplete combustion is inverse correlated with fuel efficiency (unburned fuel is wasted fuel), it's not really a trade off. What is a trade off is NO emissions vs fuel efficiency. Burning your fuel oxygen rich will burn of more fuel, but also makes more NO (due to higher temperatures if I remember correctly).

Those eventually degrade to CO2 so the increased warming from them compared to co2 by mass is temporary, like with methane.

By definition, more carbon is less efficiency. Efficiency is about how much of the hydrocarbon you turn into heat. Diesels often burn a little dirty. That's partly because diesel engines don't burn all the fuel