I mean, I assume that most people who are in a position of financial stress continue with their near-term need to commute to earn a living, and bear the cost of a tax that hurts them.

The government's job is to say that in aggregate, they people better off from the overall reduction in carbon emitted.

My opinion is that trying to make consumption taxes non-regressive is a fool's errand. If it needs to be progressive, figure out what the total dollar contribution needed and pick a rate that when scaled with incomes yields the outcome needed.