And second, if I was Paramount and I found out what JJ was pulling, he'd be fired plain and simple. Working on these two movies is a conflict of interest and I, as a producer, would feel betrayed. It's about ethics. I'd even do it to Spielberg if did this to me.
George Lucas and Lucasfilm produced Raiders of the Lost Ark
for Paramount in 1981 between producing Empire Strikes Back
(1980) and Return of the Jedi
(1983) for 20th Century Fox. I realize that Raiders
was not "space sci-fi", but it had very much the same audience demographic as the Star Wars films.
It is very common for directors and producers to work with multiple studios. There is no "conflict of interest". This is not 1940s Hollywood "studio system" with exclusive studio contracts.