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As suggested, when going through an LR section, I flag questions that I'm not 100% on. I often finish the section with a few minutes to review. As (I think) is expected, I tend to get more answers wrong in the last ten than the first fifteen, but with those few extra minutes, I'll go back to the questions I've flagged in the first half and either stick to my original answer choice, or switch it. In looking at my last eight practice tests, I've found that when I switch the answer, I'm way more likely to switch an originally correct answer choice to an incorrect answer choice than I am to switch an incorrect answer choice to a correct one. I don't usually end up with enough time to review answer choices in the last ten questions. Any thoughts on whether I'm better off trying to slow my pace down or trying to review later questions rather than earlier questions?
I also work full-time and I feel your struggle! I think it a little bit depends on what your strengths/weaknesses are, but for me I was able to make leaps and bounds in LG by just committing to mastering a single game each day no matter how late I had to work.
I used JY's advice of doing a game over and over again until you have it memorized and are able to do it calmly under the time constraints. For any game I aced the first time, I'd note "aced first time." For any game that I wasn't able to ace on the first try, I would repeat it with fresh copies until I was able to complete it confidently and within the time constraints. Once I was able to complete it confidently and within the time constraints, I would make a note "take again [insert date of next day]." Then I would take it again the next day, and note "aced on second day" or repeat the process again.
I think this also help from a psychological standpoint because I didn't get discouraged when I had a few busy days. I could count on making some progress because at the very least I was mastering one logic game, even if I didn't have time to study for other things.