Selected bin oscilation in STFT
I switched to using the normalized power spectrum and changed my output filtering from two-pass to one-pass. This appears to have made a massive difference:



It's difficult to tell from the picture but the response is actually much smoother and you can see that the selected bin is not jumping around in the same way. The two pass filtering I was using in particular caused a lot of ringing after sudden impulses and a one-pass filter was generally much, much better.