Read the passage like it's the most interesting and most important thing in your life. Well, for that particular hour, it certainly is! Seriously, my verbal went up 1-2 points as soon as my mind made that switch. I was dreading the time that I had to sit for an hour, read 7 passages, answer 40 questions that I really had no idea what they were talking about...not setting yourself up for success. At least in my experience, if you read the passage for pleasure, they actually become quite interesting and, in my mind, it became sorta like a game where I was reading for fun and trying to find that small piece of info that was going to allow me to answer that one question correctly. You know the ones, where a single word makes an answer choice correct

I also think my verbal will be higher than the diagnostic. 120 verbal questions takes a lot out of you. Some of the [easy] questions I missed were completely due to fatigue and I was just trying to get through the passages.
I second this bit of advice. I completed all of TPR verbal and I started to become really good at TPR verbal...but that's not aamc verbal. Aamc verbal isn't "harder" than TPR, it's just different. If you are really terrible at verbal, EK and TPR are great just to get you used to timing, stamina, practicing different strategy etc, but as soon as you start scoring 8+, I'd switch to aamc.
I don't know how I feel about this strategy. I think you just got lucky on that passage honestly. There have been many passages where the main idea does a complete 180 turn halfway through the passage. Humanities are like that quite often. If you get the main idea from the first half and answer questions based on that, you run the risk of getting a lot wrong. By all means, if you are crunched for time, do whatever it takes to answer as many questions correctly.
Bottom line of what has worked for me:
I practiced verbal quite often. That's the only way. Some of the [hard] questions I missed on aamc self-assessment literally came down to whether or not I picked up the meaning of a
single word. The only way you will get those, outside of guessing, is by reading the passage intently. Word. For. Word. I don't highlight, I don't passage map, I don't write anything down. I read the passage, force my mind to stay focused (that takes practice too) and I chug on through. I loosely time myself. I kinda know if I am taking way too long on a passage (10 minutes) but I can also spot the easier passages and fly through those.
For the easy passages (based on question difficulty) I generally don't go back to the passage unless it's comparing multiple retrieval bits of info. Sometimes I can answer those from memory, but often I will quickly jump back just to make sure. Any main idea or inference questions I answer from memory. This allows me extra time to really work the hard questions that require careful analysis of the passage as well as answer stems.
Post game the aamc passages. Give your mind a day to relax, but the next day, start at question 1, passage 1 and read the question stem, all the answers and explanations. Aamc gives you phenomenal explanations for why a particular verbal answer is incorrect. Don't sigh or get angry or even disagree with what they say. They wrote the test, they make the rules. Understand why a certain answer tricked you and learn how to correct it. These guys know we are scientists. They know we are always going to pick the answer that is word-for-word out of the passage. Often those answers are wrong, especially for inference questions. Heck, one of the answers I got wrong on the assessment, that was the aamc explanation! Literally, the explanation said "this answer is word for word in the passage." Granted, that was a more difficult question, but it was clearly a trap answer.
Hope this helps.