Welcome to living in a big city, NYC is not much better, I know my Sister-in-law pays $500 a month to park their car in a garage and it includes all the city taxes and such.
Personally I never understood why City's allowed so many parking garaged if they did not want you parking in the city, however they love the money they get from it all.
Personally I never heard that a government could go back in time on new taxes. They have to set them to go into affect in the future, and make sure there is public notice about the new tax. The question is did your garage never notify you all about the new tax and just now is say you all are past due, of did in fact the government make it retro active. If the government made it retro active not much you can do, pay and deal or not pay and bet your car will be towed and left homeless. Maybe it can become a home for many of the homeless families in SF.