In addition to everything you said (I do a LOT of practice questions and pay careful attention to the newspaper, particularly the editorial sections, to sharpen my skills)...
I find myself applying LSAT skills to what people say more and more. Even the most mundane TV shows, I'm taking apart what people say. Like, it might have been yesterday or Monday, and I was watching General Hospital on ABC...though I wasn't paying complete attention to the last few episodes I'd watched, which means--definitely with soaps--you miss even 30 minutes of the show and you miss quite a bit. So when you tune in again, you have to fill in the gaps by using what the characters do say. So I'm sitting there drawing inferences and making assumptions...lol...rather than running to a website that would just tell me what happened on Friday.
All this to say--pay attention to people when they talk...people around you, people on the news, people on TV shows. For example, people are always drawing analogies or mistaking correlation for causation...next time you catch someone doing that, analyze whether or not the two things being used in the analogy are REALLY analogous...see if you can find a flaw, a strengthener or weakness there...or whether just because something precedes something else that really means it caused it...because, just like the LSAT testmakers frequently like to have as an answer choice, they both could be caused to co-occur by something else.
When someone is speaking about something, pay attention to words they use and see if you can figure out their tone/attitude towards what they are talking about. Make sure you understand exactly what they are mainly trying to get across or why they are even talking about something. Think about what statements they would agree with or disagree with given what they are saying.
This helps because this is exactly what you have to do on the LSAT and what you'll have to do when you're in law school and again when you're an attorney. It's good practice all-around, and it makes for interesting conversations with people when you point out these things and also verify your reasoning through their response...because on the LSAT, you don't really get to verify with anyone...you just have to trust that you got that answer correct. Doing this should probably give you more confidence that you are thinking the right way when you take the LSAT. Plus, when people speak, their logic/reasoning/responses is/are often so imperfect that when you see perfect reasoning on the LSAT or, even, imperfect reasoning on the LSAT, it will make it easier to identify.