Well, the EU is considered canon. I'm looking for a reasonable explanation (films and EU combined), and I think that Lucas' explanation, combined with that of Anderson's, would work very well. Here's what I think: As the "Jedi Academy" books explain, a prototype death star was created to test how one would work, and to see how long it would take or something. Then, as Lucas said, once the actual first death star was beginning to be created, they had many supply problems and union disputes, which caused the process to go on for 19 years, until it was finally completed. And then when constructing the second death star, the Empire had worked out all of the problems, and could more easily and quickly create a new one in less time. Plus, you have the fact that they were using as many officers as possible to create the second one, as evidenced in the Vader/Jerjerrod conversation at the beginning of ROTJ, yet were still only half way finished, and were behind schedule.

By the way, here's a site at the Star Wars wiki which goes into details on this:

http://starwars.wikicities.com/wiki/Death_Star_Prototype