I'm encountering the same problem with working on the two Death Star scenerio.
What follows is very wordy but could be made sense of by just adding a few lines of dialogue into certain scenes like those in Jejerrod's, Piett's and Ackbar's control centres.
In ANH it's clearly stated that the original (and complete) Death Star defences were geared towards a large scale attack (presumably by capital ships).
Clearly these defences aren't complete on the Endor Death Star or they wouldn't need the shield (which is why I suggested that once the shield is down the best defence would be to move the Rebel fleet closer to the Death Star because then the super laser wouldn't be able to fire at them and the Imperial fleet would have to move in closer too creating more surface damage. The superlaser has been shown to need to be far away enough for the Death Star to target planets and ships but close enough to be in range so there would be a zone of relative safety (turbo lasers would only be able to do so much damage at close quarters and any ship destroyed would rain debris onto the station). The Rebels would have a mad dash to get out of the way as the reactor was wiped out but at least they would be safer up until that point.
With the a extra Death Star thrown in the problem if the unshielded (or surprise) Death Star had a full range of defences the capital ships (including the Executor) wouldn't stand a chance against it it would be picked off before got even close, this would make for a very short battle and a swift ending to the film. With the Rebels all gathered around the Endor moon I wouldn't put it past Palpatine to blow the planet up as soon as possible sacrificing an half completed Death Star and an Imperial fleet just to get rid of the Rebellion.
So it too would have to be uncomplete to some degree but it's edge would be it's mobility (it has operational drive systems, the one around the Endor moon does not).
So in that scenario the best defensive position for the Rebels would be to move closer to the Surprise Death Star (that way the initial Death Star wouldn't be able to fire without risking hitting the added one and as the fleets got closer it too wouldn't be able to fire because of the same reason as in the single Death Star set up).
So why doesn't the new new Death Star just jump into hyperspace when the battle isn't going to plan?
With a battle there should be a plan.
The plan in the theatrical version is to get the Rebels to attack what the think to be an anarmed station in what they think is a sneak attack, only to find they are trapped between the Imperial Fleet and an operational superlaser.
With two Death Stars the same rules would have to apply but on a larger scale.
The Endor Death Star can not move but the Rebel Fleet can so the Imperial fleet would be the defensive wall and the surprise Death Star would be the second jaw of a giant clamp.
It would shepherd the the Rebels closer to Endor Death Star by moving closer progressively closer itself.
In that instance the Endor Death Star wouldn't need to be any more than a remotely operated cannon (Jejerrod could control both from one control center).
It could be rigged that as soon as the shield is down that Death Star could automatically turn and target the moon (The resultant blast and debris would destroy the Rebels) and a coded signal would warn the Imperials to get out of the way.
This is where Lando's fast thinking upsets things in all three battle plans.
In the theatrical version he moves the Rebels closer to the Imperials (something they don't expect) which buys time for the Rebels on the moon to get the shield down so that's Lando cool grade C.
In the one Death Star but Lando dies scenerio he does the above, and rams the reactor Lando cool Grade B.
In the two Death Star and Lando dies scenerio he does both but he also totally throws the pincer plan as well. By moving closer to the fleet the Death Stars can't pick a target so they blow up their own ships (which leads Piett into self defensive mutiny).
I'm of the opinion that Piett on his own couldn't destroy a Death Star but he could knock out the drive systems of the Emperor's Death Star.
If it was already too close to the system to move out of the way if the dead man's switch fell when the shield went down, Jejerrod would have no option but destroy the Endor Death Star himself before it blew up Endor and himself in one blast.
So Lando, instead of dying destroying the Endor Station destroys the Emperor's station.
Between Lando and Piett two Death Star's are destroyed for the price of one and Lando get's the ultimate credit for throwing the Emperor's plan completely off.
That way Lando get's the Olympic Gold Medal of Coolness and we get a much more visually interesting space battle than we got in ROTS which is inkeeping with it being the final episode.
Just as the ground battle is thrown by the little people (something that the Emperor completely ignores), the space battle with all it's technology is thrown by the side-lined minor players, Lando, Piett, Jejerrod and Wedge and of these Lando is the key.