I wouldn't use carpet padding (at least the stuff I have pulled out from under carpet I pulled up), it is too soft and I suspect it won't work well. I don't know if you are using MTH realtrax with the plastic base or the stuff without it (some seemed to assume the plastic base stuff).
One thought I had might be the rubber tile you can use in exercise rooms and such, you can often buy individual tiles and it isn't that expensive, you could cut that to go under the roadbed. One of the big things (if you aren't doing this already, great) is that when putting the track down, don't use nails to hold it to the board, glue the sound deadening stuff down, then glue the track to it (if you think you may want to bring it up later, spray tack adhesive might work for the tile, the track you could use something like a rubber cement or the like). By using glue you are helping isolate the track from the board.
If the board is mounted to the wall as others point out that is a source of noise as well. At this point there may be nothing you can do without taking it apart totally. If the board rests on shelf brackets (kind of like this
------------------------ <------ board>
--------| <Wall>
bracket- - > |
|
(not an artist) You could in theory put some kind of sound deadening material between the bracket/support and the board (the white space in the picture above), but a big thing would be not to screw the board to the support arm, but glue the sound deadening material to the support arm then the board glues onto that. This could isolate the board from the wall and help deaden the sound transmission through the wall.
