Ship the optimization framework in with the application, sample from the user data, and optimize for that? It isn’t overfitting if you overfit on the data you care about, right?
Data tends to change over time, and once a hash function is in use you can't really replace it easily without a lot of overhead, possibly quite a bit more overhead than what you saved in the first place. There are some examples of this in the sorting arena too, such as 'Timsort', personally I haven't found any that gave a substantial boost, but probably there are some cases where they do. Unless sorting or hashing (and lookup) are the main bottleneck for an application I would spend my time on other aspects of it.