"J" stands for irony. The intent was to save money by building one plane instead of two or three (STOVL would mean three). They had tried this before in the 60s with the TFX which led to the F-111. The Air Force got a plane that could drop bombs, but the Navy version was a huge disappointment. In any case, the development of the F-111 was delayed, and so the Air Force decided to buy a variant of a Navy fighter -- the F-4 Phantom.
There might be something worse than the JSF, the LCS. The Navy wanted a smaller ship to operate in the littorals, but reinventing smaller ships with four different mission modules turned into a nightmare, with similar cost growth to the F-35. At least with the JSF, you're going to get a good aircraft, many in the Navy are still not sure if they LCS will provide any value at all.
You are spot on about DOD program management. All I learned about bureaucracy came from reading about came from DOD program management -- and War/Navy Dept. before the creation of DOD.
Still, calculating life cycle costs can't be easy when aircraft continue to fly long past the expected end of their service lives.