1) Why don’t the rebels evacuate the base just in case? A skeleton crew would have to remain behind to coordinate the attack on the Death Star, but they can do that from a ship, and everybody else can be getting the hell out of Dodge at light speed, leaving the Death Star nothing to destroy but an empty base.

2) The Death Star spends 30 minutes orbiting the planet to get a shot at the moon. Wouldn’t it be a lot faster to just blast the planet? Judging by the debris and shock wave resulting from the destruction of Alderaan (in the SE and later editions), the explosion almost certainly would take out the moon. Even if it doesn’t, it would leave the Death Star with an open shot at the moon. At the very least, the moon would be rendered uninhabitable and the base useless; people and ships might have a chance to get away, but they should be gone already anyway, especially if you give them an extra 30 minutes to evacuate while you circle the planet.

And talk about an “effective demonstration”! It would say, “If you harbor Rebels in your system, you’re dead, no questions asked, so you better be vigilant about not letting Rebels use your system.”