One thing that nobody seems to have suggested for congestion charging is somehow scaling the charge by income. A trivial way to do this is by charging differently for different types of cars, but there are more direct ways to link the charge with income as well. The advantage of this move is that it at one stroke completely gets rid of the opposition's "what about the poor people who can barely afford a car" argument. And scaling charges to income is not completely without precedent: fines for traffic violations in Finland work like that, and some Nokia executive got a million-dollar speeding ticket once.
How about giving low income folks free passes for the transit system and cutting all fares for everyone else?  Have the congestion charge make up for the lost revenue.
London again.

Revenues from the Congestion Charge haven't met expectations.  Traffic fell by more than expected (but not at peak hours).  Costs of running the system have been higher than forecast.

Meanwhile the system is flooded with low cost users (kids under 16 are free on buses, also those over 65 etc.).  But the transit system (at peak) is 100% capacity.  Kiley (former head of the NY Transit, imported to run ours) told the Mayor this would happen, but our Mayor is an ex Trotskyist demagogue (think of him as a Rudi Giuliani of the Left).

Another nuance is we now have double length 'bendy buses' to replace the conductor on the old Routemaster double decker.  As a result (you get on and off at any door) I would estimate at least 1/3rd of riders are not paying (you don't pay a fine often enough to make it worth paying).  Maybe over half of riders on some routes.

Difficult to administer and too easy to cheat, I suspect.

Scandinavian societies are high homogeneity, with high compliance to laws.  New York is a high heterogenity, low compliance to laws kind of place (OK it's not Lagos, but compared to most major western European cities).

Systems and social programmes that work in Scandinavia and in Singapore, don't work so well in freewheeling 'Merica.