Based on the answer to the question you referenced, and the question of why the Death Star had to wait for a clear shot, I think you're focusing on the wrong details of the quote you refer to.
After firing a blast, though, the Imperial engineers had to recharge the reactor, which took at least 24 standard hours. Though the energy output of this blast could be scaled to fire at smaller targets such as capital ships, as was the case during the Rebel assault on the second Death Star, the two major instances in which the superlaser was fired were at full power at planetary bodies.
We see during the Battle of Endor that the Death Star can fire more than twice in 24 hours, it just needs to be used at a lower setting. It's entirely possible that the Imperials didn't intend to use the Death Star at full output, and only enough to destroy the Rebel Base. This would explain why the Imperials needed to wait to get a clear shot.
This is backed up by the Death Star Tech's dialog during the battle as they approach. They first mention approaching the moon, but then start referring only to the base itself.
DEATH STAR INTERCOM VOICE
Orbiting the planet at maximum velocity. The moon with the Rebel base will be in range in thirty minutes.
VOICE (over speaker)
Rebel base, three minutes and closing
DEATH STAR INTERCOM VOICE
Rebel base, one minute and closing.
DEATH STAR INTERCOM VOICE
Rebel base, thirty seconds and closing.
DEATH STAR INTERCOM VOICE
Rebel base, in range.
TARKIN
You may fire when ready.