The floss mod is not as nice on a Model M as on an F, but it does not have to harm the action.
If the floss completely fills the spring, the effect is the greatest. Cutting it a little shorter, say, 2/3 to 3/4, will cut the noise almost as much and affect the action less (remember that it has to be more than 1/2 because that is where the spring actually buckles!).
Packing the cavities with soft fluff of some sort will help, but running something like duct tape or rubber cement on the inside of the case will deaden the actual vibrations of the "sounding board" itself.