I very strongly believe that this is a case of barking up the wrong tree as far as what the culprit might be in terms of why a feedback section might seem harsher on one playback than another. I'd much more than likely peg this as being caused by the listener being in a different spot in the control room causing some frequencies to stand out more (see
Why We Believe for further details on this point), - or by monitoring at different output levels on the before/after playbacks than to being caused by requantizing. Harsh frequencies will sound much harsher if listened to slightly louder.
First off - do a null test between the source 24bit file and the requantized 16bit file. If there is anything different between them occuring over the -76dBFs level at the very maximum then this is an indication that something is broken in the DAW app or in the dithering algorithm. If there really isn't any difference between the two except at the -80dBFs and lower level - I'd suggest you rethink your idea that dither is capable of making things suddenly "harsher." Some blind a/b/x tests might be in order also.
Best regards,
Steve Berson