Keep the stock heat shield in place. Heat shields are multiplicative in reducing heat transfer by radiation, while also limiting convection. The stock heat shield will only help keep the heat in better, away from your hood and intake tubes.
The additional DDM heat shield installs by replacing one of the bolts of the stock heat shield with a threaded stud. It's a pain in the ass to get to it. I found it best to just tighten the nut onto the threaded stud to keep the stock shield in place and to make sure the stud is always nice and tight. That leaves my DDM heat shield loose at the bottom connection point, but I haven't had any issues with rattles. I have to remove the extra heat shield any time I change between downpipe/first cat; this makes it much easier.