That actually does sound like something J.R. could have done. He cared enough about the idea of not wanting one his children to be born in prison to a convinct that he agreed to cover for Kristen and not press charges. So I imagine he'd also not want Kristen raising his child at all. So when he banished her to L.A. he had people following her, and when she was in the hospital about to give birth, he paid off the doctors and nurses to have then steal the baby right after birth and tell Kristen it was stillborn (back then, I think most women were still giving birth while under anesthetic, as opposed to "natural childbirth", so they could have pulled that off while Kristen was unconscious), and since he knew he couldn't explain a new child to his parents, he had the baby raised in secret.
Of course that would have knocked out the Christopher storyline, and how Bobby got him originally believing he was J.R.'s, but they could have still just had Bobby and Pam adopt a baby the normal way.
Well in Hunt's case, I think he just went ahead and married some other woman who didn't know whom he really was, and kept them all secret for awhile. If they hadn't written out the reuinion movies, they could have gone that route with J.R. Remember the 5 years he spent in Paris in between the series finale and J.R. Returns? Say during that time he met and fell in love with some French woman. Maybe it was just short and volatile (because J.R. was still mostly focused on his long-range plan to eventually return to Dallas and get Ewing Oil back), and they ended up divorcing just before J.R. returned to Dallas, and the ex-wife discovered soon after that she was pregnant, and gave birth to a daughter (which J.R. would occasionally fly back to visit, but never told his family back home). Timing it right, that daughter would have been just recently turned 18 at around the time Dallas Season 3 was ending, thus eligible to recieve whatever inheritence J.R. left for her (maybe some stock or land-rights now worth billions). And that's what made John Ross interested in tracking her down.