You can also try bracing the rear of the player. Sometimes just the front mounting point of the kit isnt enough. Some kits have better support for the sides than others. There should be a place to attach a metal bar to the rear case of your unit.
Also, make sure your front mounting points are secure. Sometimes the problem really is the player. Cheaper players simply do not have enough shock absorption built in. You want the install to be as rigid as you can get it, and let the internal shock absorption of the player handle the bumps.
The foam isnt really the best of ideas. Dont forget that the player gets hot at times in there, and you want it to be able to circulate air around it, or risk it burning up. Plus, some foam will trap moisture in there as well. A small piece or two should do the trick, but dont go nuts with it and stuff a ton under there.