Being that you have been floating theories, how about this one. Note I am useing your habit of numbering items.
1. Howard was replaced by the CIA after the 1946 spy plane crash.
2. Jean Peters was a plant by the CIA to insure that if the "plant" for Howard got killed in a public accident they could still control his assets.
3. You obviously are missing some major pieces with the players here or you would be getting a lot of positive results. Just bear with me and you may get a new angle.
4. Now when you interviewed Shirley she said, "Jean did not have any children." But Richard muttered under his breath if copy of this is accurate, "At least not by Howard Hughes." Let's assume both of those statements are true, then Jean may well have had a child by the man she was living with and who she married. He could well have been posing as a "fake" Howard but a "real" husband to Jean. Ergo! The problem of making this pregnacy public. The child wasn't Howard's and if someone in school got wise and did blood tests or as DNA became available to the public, he was tested, then the whole CIA scam would colappse! Ergo: the neccessity of keeping both the child and the pregnancy secret! Richard, through trying to not tell an outright lie may have given you the real clue you need!