As we always function, I will chip in my two cents and others will add to it and the accumulative answers will give you a good all around plan.
Phillip, much depends on how much weight you intend to add. And how important it is to dispurse the weight around so that there is not one tight spot with all the weight.
Personally, I did not see Bob's special on beef ups, but I would say that 2x6's on 16 OC should be fine enough for the basic storage. I do not know how you could add support unless you sister and run the sister board the entire length of the sistered board.
What I would do is what I practice myself. Your attic is the most supported if you will where there are walls below for up right support. I have a situation where I have built a small catwalk to an area where three walls are about 4 feet apart. There is where I built my storage spot. I don't have any sag, don't have any un supported areas. I have no telling what is up there. And Phillip, my home is 35 years old and my ceiling joists are 2x4's 24 inch OC. I think you are ok to a reasonable extent.