I'm pretty sure this is exactly what op is saying, isn't it? The toll forces poorer people to change their behavior while letting rich people continue to do what they've always done with a barely noticeable dent in their wealth.
Instead it's now a consumption tax which is regressive. All the rich neighbourhoods have large bins and it costs them less than a property tax increase would have while the poor neighbourhoods all have to "budget" their trash to fit it into a small bin.
It's all a way of forcing the poor and middle class to bear the burden of dwindling resources and infrastructure while the rich get to maintain unfairly luxurious lifestyles.
For example a VAT is regressive, but is usually accompanied by a rebate that sends a cheque to everybody for an amount that a typical poor person would spend on VAT. The congestion charge goes to the MTA, which benefits everybody.
For your example, where are the proceeds spent? If the charges are spent to improve everybody's garbage service, the rich people paying the surcharge are paying to improve the service for everybody; the rich are subsidizing the poor.
How does the math on this work? If a regressive tax affects poor people disproportionately over rich people and you then turn around and spend the proceeds on something that benefits everyone equally, you've just done wealth redistribution from poor to rich, no?
In order to counterbalance the effect of a regressive tax you would need to spend the proceeds on something that benefits poor people more than rich people so the disproportionate negative impact is balanced by a disproportionate positive impact.
Arguably paying for the MTA may count as doing that, given that poorer folks are more likely to be using it than rich folks (especially now post-congestion tax). The congestion tax becomes a tax on what is now a luxury (driving a car in Manhattan) that is used to pay for a staple (public transit).
But they're still regressive taxes. Poor people spend a higher percentage of their income on stuff than rich people do. It's less in absolute terms, but more in relative terms.
If the taxes earned from these transactions are then spent on things that also benefit the wealthy just as much as they do the poor, then the rich are double-dipping and poor people still end up net behind the wealthy. They lose access to something that previously was paid for out of property taxes in exchange for more revenue funding services that the wealthy are just as likely to use.
This model at least doesn't further exacerbate the regressiveness of the tax by only funding things used by the rich, but it doesn't restore balance.
That's why I say that the only way that you flip the tax to be progressive is if the proceeds benefit the poor disproportionately rather than benefiting everyone equally.