I don't have my Service Manual here, but if you go by the book, it is a lot of tedious work to get all the way to actually removing the dash, and I mean the car needs to be nearly gutted(see Dash Removal in the Body chapter). Taking the bolts out of the ends will still leave some fasteners in the middle, which are only accessible with the trim removed. It is conceivable that you could shove some felt into the crevice between the dash and the mating piece holding the pin sockets, using a putty knife. Certainly way less involved than dash disassembly, even if you loosen the end bolts to get a little play. Be warned that normal dash removal involves removing many things, even the glove box, steering column, radio, clock, CCU, and much more, so don't try to move the loosened dash by more than a small fraction of an inch.
If felt is not your thing, then maybe you should try the leather/vinyl treatment route as mentioned in this thread, and in the FAQ, if I remember.
Here's to a quiet dash for you....
Regards,
Bill