It seems like you are in a same situation that I was in about a year ago... well almost. I'm Korean myself and English is my second language. Been studying for LSAT and will be taking it in October.
I have to say TM is not very good at teaching RC and they barely have any strategies for that section. They are very good at LR though. Are you aiming to answer all the questions in each section? Perhaps you might want to focus on answering less questions and increase your accuracy. For instance, if one of your LR section has 26 questions, then you might want to focus on answering only like 20-22 questions (even less if necessary) but devote more time on individual questions. Same goes for RC. If your current strategy is to go through all four passages, you might want to cut it down to three but answering the relevant questions with more time invested in each.
For RC, if you are to answer all questions (26-28) you should be able to go through the passage in like 3 but no more than 4 minutes while picking up vital information: topic, author's tone (if he or she is present in the passage), positions (i.e. are there proponents or critics to certain view mentioned in the passage), conclusion, how the conclusion has been reached, etc. I don't know how many passages you've tackled, but you'll notice (or have noticed) a pattern that is taking place in the RC section. Eventually you'll be able to tell what kind of passage it will be just by reading the first paragraph once you see this "pattern."
I also believe that your attitude when answering these questions matters. Tackling the questions with confidence will greatly improve your score (it worked for me at least
). I'm assuming that you're pretty good at LG as you've not mentioned it as one of your "weak" sections? If so, then perhaps you might want to check the difference in your attitude when tacking LG and tackling other sections.