I spoke with Judson Scott (who played Joachim) at a convention once. He believed that Joachim was indeed Khan's son and that's how he played him.
And you and I discussed this online before you wrote the book, and it was such a buzz to hear you formulating your plan of attack for how you'd handle events; Judson was a guest at an Aussie con in the 80s - I had to break the news to him (the morning he arrived Down Under) that "V: The Series" had just been announced as cancelled. He'd been told that Lt James was about to get his own ship in Season Two! Ooops.
Judson was invited to Ricardo's house when he was cast and they did script readings together, establishing for themselves their backstory, as actors often do. In a "Starlog" interview, he says of Khan: "He's my Daddy!"
There was a painting prepared as set dressing, though: of Marla (ie a self portrait), Khan and the little kid (who was seen at the porthole in the cut footage), indicating that not too long had passed between Marla's death and the events of ST II, but of course the pic was not seen on screen - and neither Judson nor Ricardo knew that it was created when they worked on their backstory.
I rather like that the Ceti eels went rampant after the planetary orbit shift.
Since this had never been "officially" established, I split the difference and made him Khan's foster son in the book.
And it works rather well. Some people guess that Joachim in ST II is simply an Aryan-revised, misspelled version of "Space Seed"'s dark-haired Joaquin (Mark Tobin).