We ran several simulations of filter designs during prototyping. We very quickly came to the general idea of using several bandpass filters to handle various bands of frequency separately and then combine the outputs together using a summing amplifier. It took us another week to settle on the filter design and parameters as well as the number of filters. We eventually settled on 6 1st order bandpass filters with center frequencies evenly spaced out between 250Hz and 10000Hz. This gave us the following design.

If we modify the resistor values of each filter we have total control over center frequency, gain and quality factor, though the "standard" values shown give a smooth, neutral amplification:

If the user needs amplification at high frequencies we can modify the gain resistors to get the following response:

We also studied the possibility of chaining the filters by passing the output of one to the input of another. This would give us a higher roll-off rate and could be used by adding some switching circuitry. The use case of this would be a user with a significant amount of hearing loss in certain bandwidths and no hearing loss in others. In this case, we would not want to overamplify the bandwidth in which their hearing is not impaired.

An example response is like this: 

Here, the roll-off rate is twice that of the previous filter and has useful amplification only in the requested areas.