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So my RC is my worst section and I do not really feel that I can improve much on it. But I still have a lot of room to approve in LG and LR, should I focus more on those sections? Or give at least some time to RC?

People generally say RC is the hardest to improve on and LG is the easiest. That said, your LR prep will probably also help with RC since a lot of the "main point" and "role" type Qs show up on both.
Another user recommends reading an article from the Economist or another quality news publication, then opening up a word doc and typing everything you remember including listing the main point of the article, the main points of each paragraph, any support the argument relies on. Many people advocate doing a lot of critical reading in addition to actual practice RC sections and this would probably help if you feel like you're in a rut.

Nope, not wise.

sleep less
and make time to do RC

I did this for the recent February administration. Leading up to the exam I barely did any RC work or drilling until 2 weeks to the exam date. Even then, I wouldn't really review my RC sections and I focused primarily on LR/LG. As I had to bubble in guesses on an entire RC passage, lets just say that I regret it.

I will have to take June again, this time focusing on LR/RC and sprinkling in LG occasionally. But I will utilize this advice http://www.top-law-schools.com/forums/v ... 6&t=203798 for RC.

RC was my worst and I spent months doing the Cambridge RC by type book. My RC improved some (active reading for main point and role questions got better) but for some reason the RC helped me get much faster in LR. So in the end RC prep helped a lot, just not in the way I thought it would.

Manhattan LSAT RC guide, the only one I've found useful in my experience.

That one's Reading Comprehension ability is fixed - and thus cannot be improved - is an LSAT prep myth. It can be improved, but gains in this section are often harder to come by. I have seen students improve their RC drastically.

Since this is a particular area of weakness for you, I'd suggest spending more time on RC, not less; Michael Jordan spent most of his time in the gym drilling the (relatively) weaker parts of his game, not the many areas that were strong.

RC isn't even that much about Reading Comprehension. A lot of it is still logic and compare/contrast.