My 2¢:

I'd definitely add in "The Rebel Alliance has been driven to the fringes of the galaxy." at the beginning. It sets up the current situation for the Rebels, just like the first two films did. ("It is a period of civil war." and "It is a dark time for the Rebellion.") And it grabs the audience more.

Also, your second paragraph fails to mention Han at all. On top of that, "Upon learning of Chewbacca's capture" is just a better-written, more active sentence than "Learning that Chewbacca has been discovered and captured." Plus, it's slightly shorter. I'm indifferent on "Lando has sent a desperate message to Princes Leia" versus "Princess Leia has impatiently rushed to Tatooine to free her friends" - I think I lean more toward the latter, but they're both good.

Finally, I'm also indifferent toward "certain doom for the galaxy" versus "certain doom for the small band of Rebels struggling to restore freedom to the galaxy."

Here's my compromise attempt:

STAR WARS

Episode VI
RETURN OF THE JEDI

The Rebel Alliance has been driven
to the fringes of the galaxy. Still burdened
by the terrible truth of his father's fate,
Luke Skywalker has returned to
Dagobah to complete his Jedi training
under Master Yoda.

Meanwhile, in a daring attempt to
rescue Han Solo, Lando Calrissian
and Chewbacca have infiltrated
the court of the vile gangster JABBA THE
HUTT. Upon learning of Chewbacca's discovery
and capture, Lando has sent a desperate
plea for help to Princess Leia.

Little do they know that the GALACTIC EMPIRE
has secretly begun construction of a new
DEATH STAR. When completed, this
ultimate weapon will spell certain doom
for the galaxy....

This formatting actually uses fewer lines than the 1977 Star Wars crawl, so you shouldn't have timing issues.

--edit--

I'm not sure why we have a "center align" button when it doesn't do a damn thing, but whatever.