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As far as identifying my “problem sound” with a technical term, I’m now quite certain that it would be called “clipping.” I verified this by watching a YouTube video in which a guy discusses and demonstrates audio clipping (as it relates to a high-end video camera microphone). The samples of clipping that he uses (with voice, solo instruments, music) leave no doubt to me that that’s what I’m hearing.
Maybe this will help you experienced guys in steering me towards the most viable of the several fixes mentioned above. (It could get pretty expensive for me to work my way through the fixes!: buying a low-pass filter, buying that transformer gadget…)