My approach is to let the "bins" collide at the filter bank level (really let nearby tracking resonators agree on the dominant frequency in the neighborhood), and use the bank's instantaneous state as input for a frequency component tracker, whose output is a list of (frequency, amplitude) rather than an array of bins.

Here is a short video demonstrating the concept (with spectrogram-style visualization): https://youtu.be/STayypC1pvU

This is all pointing towards a dynamic systems approach, with prediction/feedback loops, e.g. establishing a tonal context and feeding it back into the analysis.

I believe some plasticity in the natural frequencies in the bank and tuning of the resonator dynamics would improve the convergence time to some extent, but I think this will only go so far and most of those effects should be addressed via prediction/feedback.

I envision the timbre analysis to take place on these tracked components as well as harmonics should be tracked as components whose frequencies are multiples of a fundamental (so analysis on actual small number of actual frequencies rather than a large number of bins).