Wasn't he also already set to direct something else during the shooting schedule as well?
No. He had just finished E.T. (and POLTERGEIST, as Producer) and was Exec-Producing TWILIGHT ZONE. He didn't direct again until TEMPLE OF DOOM, which shot in 1983 (which would have been after ROTJ).
And in case anyone was wondering why the DGA issues prevented him from doing SW but not INDY...
The issue actually arose in 1980, when the DGA filed suit against Lucas because he used a guild director (Kershner) but did not abide by the guidelines of having the director's name on the opening credits. They also fined Kershner. As you know, the SW films don't have opening credits. Lucas explained this, but the DGA held firm because they contended that the "A Lucasfilm Ltd. Production" credit that did come before the film was giving the Producer a credit (Lucas) but not the Director. It was okay to them with SW in '77, because Lucas was the director. But they jumped on him for EMPIRE. He told them to pound sand, paid Kershner's fine, and resigned as a member of the DGA & WGA.
When ROTJ was in prep (1981), this was still a very fresh, sore issue. Spielberg, as one of the most prominent members of the DGA and powerful Hollywood mogul, would have been forced to basically blow up the industry union status all on his own had he signed on to do ROTJ.
This was never a problem with the INDY films because, a) They did have the credits at the beginning and b) While Lucasfilm productions, they technically were made within the Hollywood studio system at Paramount.
The guilds are obviously much less ridiculous these days about that stuff.