I'll leave it up to you guys to determine what ought or ought not to be done with that rig. But if it were to be tested for DNA, a couple other places to test would be the underside of the shoulder part of the harness, as that is the most apparent and common way of picking it up, and also the pin protector flap on the back of the backpack. Along the edges of that, especially where those five snaps are that hold it closed. If Cooper knew enough to do a full pin check on it, he would have opened and reclosed that.
All of these areas would also have been touched by the rigger that did the two repacks after Hayden got it back.