I'm just studying for my first LSAT myself, and had been having the same problems as you describe. With some intensive work in the last couple of days, I've been able to drop my time to finish the LG section on my daily practice test from 35-45 minutes (ack) to 25-30 minutes.
I've found the analogy to language learning helpful. You're at that point where you know *how* to say a lot of things in -- let's say -- Japanese, but you have to stop and think about each word. Of course, it's no good knowing how to ask directions somewhere if it takes 5 minutes to finish the sentence.
So the next step is fluency practice: working over and over on stuff that you already understand, until it becomes automatic. Now, if you're actually planning to spend 13 months preparing for the LSAT (not nonstop, I hope), you're going to want to husband the real practice tests, since there are only so many. So one thing you may want to do is look into non-authentic practice tests; you can find these in any LSAT book that advertises practice tests but doesn't mention where they come from
. These aren't valid as diagnostics -- they'll be too easy, or too hard, or just too non-LSAT-like -- but they're similar in type, and you can sit down and take, say, 3 LG sections in a row without worrying that you've taken 3 whole practice tests out of circulation.
Alternatively, you can go back to practice tests that you took a little while ago -- long enough ago that you don't remember the details -- and use the LG sections from those. Either way, repetition is key to building fluency; your brain needs lots of practice in order to get up to speed with this kind of unfamiliar material. (And if you're like me, your brain needs a lot more practice on LG than the other sections.)
Anyway, YMMV, but I've had good results with repetition+persistence so far.