You are correct, it would be on a contigency basis. And you are likely correct, there are probably very few cases involving private attorney's taking a case such as one of these on a contingency basis unless it was pretty clear the venue was in the wrong. And most of us don't have the money to hire one to pursue the case otherwise.
I'm not aware of any part of the ADA related to accommodation for hearing loss that would address noisy restuarants.
I have read about some HLAA groups around the country who have been involved on the front lines with legislation related to hearing loss issues. Washington State's HLAA group was at the forefront of working on getting a law passed requiring insurance to help cover the cost of hearing aids. Sorry I don't have other examples right at hand.