Red Superfly
You creepy little stalker
Makes total sense now.
I doubt the blueprints thing would ever be a major problem. A contributing factor, yes, but a major one? No.
The major problem would be: The Senate.
When The Death Star is first made, The Senate is still intact. Only by Episode IV, when the Death STar is completed, can the Emperor keep the systems in line with fear, as Tarkin states. Until the Death Star is completed, The Emperor NEEDS The Senate to maintain control. First Death Star: Emperor + Senate call the shots and argue and bicker. Second Death Star = Emperor calls the shots DIRECTLY.
The two decades or so it takes for the first Death Star to be finished is totally believable. God knows how many protests and negativity was directed toward the project. It was probably put on hold many times due to the Civil War and the Senate alone. This is something I hope the TV show will touch upon.
Once the Death Star is completed, Emperor can do what he likes, nobody would dare oppose him. But until that moment, he has to put up with cutbacks, The Senate (which also aids the Alliance from within)
However, with the Second Death Star, The Empire is already a dictatorship. The Emperor can pour as much man power onto the project as he likes, as hard as he likes, has has total control by then, which is why the second one is fully operational in a fraction of the time.
Also note that The Emperor was sending Vader out to be the slave master, cracking the proverbial whip to get the second one done. He couldn't have pushed people around like that with the Senate intact. It all makes total sense. I used to think it was down to the blueprints and stuff, but it's really down to the resources The Emperor had at his disposal at the time of each project.