Jessica, I'd go from the gentlest method, brads hot water bath, to the bristled pipe cleaner, to the soft wire.
If all else fails, the replacement stem sounds like a good plan C or D. But I suspect the hot water will do the
trick. In my experience, Q-tip cotton reduces in size when wet, unlike rice kernels for example that expand greatly.
(Irrelevant detail: Some old sailing ships carrying casks of dry rice had their hulls split in half when the hold flooded
because of the expansion of the rice. Horrible thought.)