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This turned out to be easier than I expected
The main thing is not letting the left and right channels get time stretched/squeezed independently, which you can do with this nonsense. Less obtusely you can think of it as doing the algorithm on the average of the left/right channels instead of each independently, and then applying the change it wanted to make to both channels. And actually you could do exactly that, but I don't, because it helps masks an annoying issue to do with the way uncorrelated audio mixes, which makes certain noisey songs sound fluttery
The algorithm this thing uses still has a more fundamental issue which is on uprates it will just straight up skip beats. There's really no good reason for this but I don't think it can be fixed without just rewriting it entirely