ugh I hate it when I can't sleep. warbonnetguy... the dierections you were given are excellent for resoling shoes. The devil, as you say, is in the details. When resoling shoes the really porous materials of the shoes have already been sealed with the previous coats of adhesive. In the case of the foam pads the surfaces are both raw and unsealed. The foam is likely porous and pebbly for lack of a better word. The nylon is porous and can tend to ravel. My experience in this kind of a situation, making scenery and other off label uses for the Barge would suggest that the surfaces be sealed with a thin coat of Barge which is allowed to dry completely. Then another thin coat can be applied to the prepared surface to do the actual bonding. The heat applied to the shoe barely softens the adhesive allowing it to tack together securely. In the case of foam or other heat sensitive materials allowing the second coat to be barely tacky accomplishes the same goal. Barge is very liquid as it comes from the tube or can. In the process of spreading it around you can easily create drips along the corners of the pad. Those drips are bad news if they should bond together. The mallet and plywood is simply an easier way of applying solid pressure to the bond when wide or large surfaces are being bonded. Not everyone has the clamps to pressurize the bond and books can be dubious. Wailing the snot out of the bond with a mallet exerts more force and the plywood distributes the force over a wider area.
Lest anyone be confused over seeming differences between my suggestion and what warbonnetguy posted should recongnize at this point the instructions are very similar once the surface prep is accomplished. Barge is very potent stuff. Thin coats are all that is required, but the raw surfaces are better if sealed first.