You could also have tax paid off over time. E.g. a concrete building that lasts 60 years, vs a stick build that lasts 20. Bricks are frequently recycled, >100 year lifetime.
I'm open to hearing counter-examples, i.e., where there is an external cost to not manufacturing a high CO2 cost product. The examples I've seen so far are really arguments about competition with BRICS economies, and their bizarre exemption from controls.
That customers will feel price pressure from their most-carbon-emitting activities and commodities is precisely the point. This will encourage finding alternatives. No demand is entirely inelastic.
Squeezing extra tax out of poor people who have literally no alternative is not going to be a popular plan. Allowing for a hint of nuance in your public policy would incentivize switching to alternatives where possible, while also incentivizing the development and adoption of alternatives where they don't currently exist.
I am highly skeptical that is it possible for American legislation's 'nuance' to tilt a simple tax law in any direction but towards enriching the rich and powerful.
I feel like carve outs would be great for lobbyists and the politicians they pay patronage to, but it would destroy the effectiveness of the carbon tax: the industries with enough political power would negotiate exemptions because "there are no economically feasible alternatives" but making carbon-expensive activity economically infeasible is the core purpose or the carbon tax.
Exempting any industry in particular is just corruption.
I think a carbon tax with dividend actually fits the criteria you are describing pretty well.
If the amount of the tax were fixed, the dividend would decrease over time, but the tax gradually increases as we get better and better at doing things without emitting greenhouse gases. The eventual target being net zero carbon. Based on the tax level in the Energy Innovation Act as an example, this is predicted around 2050.
As to your second point - moving the goalposts every time progress is made eliminates any incentive to improve. If you're committing to keeping the dividend the same over time, that means you need to keep the tax take the same. And if you're gonna take the same amount of money off me regardless, why should I pay attention to my emissions? In the limit case, of zero carbon, the carbon tax rate is infinite and you're taking a bunch of cash off people for nothing. Somewhere along the way, something has got to give.