Actually there's an alternative to converting the parallel filter to cascade filter, which is just to keep it as a parallel filter. How this can be done I will describe shortly. This may be preferred as I believe not all allophones can be modeled well by cascade filters. Furthermore, perhaps higher resonances can't be at all in general.

The parallel filter is just a sum of resonances, which are each linear-time invariant filters, thus it is also a linear-time invariant filter and thus also can be expressed as a z-transfer function. This can be done in practice by starting with a z-domain expression of the collective z-transfer function, in the form of a some of all the composite z-transfer functions. Then, each of the terms are refactored such that they all have an identical. Finally, all of the numerators can be summed. Much of the terms can then be combined since they are just constants times some power of z. The result is an IIR filter.

We can use the decomposition property of IIR filters that lets us turn one into an all-pole IIR filter and an FIR filter that represents the zeros. We do the inverse filtering step using the former. Finally, we add an additional step in the second WBHSM pass where we divide the spectrum by the latter's frequency response.