It's kind of funny this topic is discussed at Smogon, with love of long analyses so prominent (and necessary). It's also one thing that drew me to this site.
I'm going to interpret the struggle with "terse and simple" and "churning out prose" as seeking methods of writing stylishly without fluff, in a reasonable span of time. I'll also assume you've gone through the structures and junk that school (high and college) taught you. With these two points as a given, I'd say you should take what you know, and break the rules just enough to find your own "voice" in writing. In my experience, the more your writing resembles your speaking, while retaining elements of being printed text, the more natural you'll feel at churning out your prose. Whether this sounds conversational or not is another story. Some people never sound conversational. Others do. No one can tell you, through precise steps, exactly where the fine line stands for you as an individual, and it is also my belief that this is why writing takes so long for some to master, while others serendipitously get it so quickly. But once you do, it gets a lot easier.
And a lot harder. I can crank out tons of text myself in a short time. I never do. This post alone will take me a while, since I try to minimize useless words, examine whether my views are expressed well, and consider my tone. If my tone is non-threatening, explanatory, and friendly enough in this post, I should be able to say, "Shit, fuck, damn, and piss," and still sound somewhat professional. The digression aside, I have always felt that writing efficiently may not mean printing out five pages in half an hour. That has always seemed to be finishing an assignment quickly.
Writing efficiency stems from communicating effectively. That doesn't always take such a short while. Good warstories are an example. Even if the time isn't spent on text, it may be spent on formatting, so the story itself is told clearly and captivating. The question boils down to how much quality you also want for a given piece. It's directly proportional, in my opinion, to how much time you must spend for your results.
Since my post is a bit long, I'll restate it in a few tips, that have helped me for a long time, in school as well as business (note the self-referencing change of tone here, since I'm communicating to people who may just want the bits without the thought behind it):
1. Write the way you'd sound. Don't front.
2. Edit the fuck out of yourself if your piece is worth it.
3. Semicolon ftw.