I have a few suggestions, probably none of which will seem revelatory to you.
1 - Stop "faking" interest, and take a real interest!
Easier said than done, but I honestly believe that this skill is incredibly important not only to LSAT reading comp, but also to all the reading you'll have to do in law school and to being a well-rounded adult.
This world is incalculably rich and complex, and our lifespan / brain capacity is such that we'll never have a chance to experience it all. When I read RC, I honestly embrace the opportunity to dive head first into a topic/specialty that I would typically never read about or know about.
You may have read that particularly boring comparative RC passage about drilling muds. You gotta have a sense of humor about how droll and obscure LSAT will get. Seriously, drilling muds?! I've never once contemplated what factors go into selecting a drilling mud, but now, thanks to this passage, I have some random glimpse into someone else's profession. (It's like the written version of watching "Ice-Road Truckers" or "Swamp Fishing")
By being a more receptive reader, you won't necessarily memorize all the nitty-gritty details. Some ideas will stick better than before. But mostly you'll have a better memory of where specific things were mentioned. When it comes time to researching Inference answer choices, knowing where in the passage a specific phrase was used is a big time saver. That way you can quickly check on the actual wording in the passage and compare it to the answer choice.
2 - Look out for extreme language. By far, my biggest crutch in RC is the fact that my brain immediately scans answer choices for the most dangerous wording. Extreme language and comparative language are SUCH frequent giveaways for wrong answers that they do wonders at trimming down a set of five answers into the 2 or 3 likely candidates that are worthy of closer investigation.
Some examples of potentially dangerous wording:
"most, primarily, usually, generally, tends to, often, requires, needs, necessitates, only, unless, all, none, never"
3 - Prove all your answers to yourself. Make RC right/wrong into something objective, not subjective. The best way to do this is to justify every correct answer with a line reference and to identify a specific word/phrase in each incorrect answer choice that breaks it.
Being this thorough for all 5 choices will initially seem like too time-consuming of a process, but this is the skill-set you want to develop. You'll get faster at scanning for your proof sentence and faster at identifying the broken language. And when you end up getting an answer wrong, you'll compare it to your proof sentence, determine why one is not equivalent to the other, and thereby refine your ability to measure wording from the passage against paraphrases in answer choices.
Hope this helps.