I had the same problem in South Florida (before I moved there). A surprise cashless toll road -- taken in error -- in a rental car cost me $15. Then in 2014, I made the completely unavoidable mistake of driving south over the now-cashless Golden Gate Bridge in a rental car. This time, the $7 toll cost me almost $40!!!!! I was really furious about that one. There was no reasonable alternative route and no way to pay in cash or even by credit card. This is a problem that really needs to be solved. One solution would be for the car-rental companies to charge back only their actual costs and not let third-party billing companies triple or quadruple those costs at our expense.
Bruce