The reason Kirby doesn't own the New Gods characters are clear. He sold the rights to DC, he had a contract with DC which defined the working relationship. It's similar to the situation where Kirby signed a clear contract with Marvel in 1975.
The estate could try and regain the copyright to the New Gods characters, but it's to soon to file that claim, thats why the claims concerning the Marvel era characters covered the years 1958-1963.