Can anyone explain to me why my bare shafts fly quietly off the shelf and my feather fletched arrows make a slapping noise?

I've played with brace height and nock point to extremes but nothing seems to work.    

Two possibilities I can think of:

Adding feathers and glue to the rear end of the shaft does increase stiffness slightly.  Try using a heavier point and see if the slapping goes away.

You could have quill contact with the shelf or strike plate, which could make a noise you might interpret as slapping.  Try cutting the feathers off an arrow but leaving the quills attached.  I know, nobody wants to ruin an arrow, but having an arrow with just quills attached is a lot better than just a bare shaft anyway, and will be useful to you in the future.  Take the bare shaft you were going to save and put feathers on it, and you'll be even.  Put lipstick or something on the quills and see if it makes a mark on your strike plate or riser.  If so, rotate the nock and shoot again until no quill contact is being made.