I also got a 36 on science, and I always read the passage first (and I finished with about 4 minutes to spare). Apparently skipping the passage works for many people, but I prefer to read it. See which method you prefer.
I agree that you should learn to identify the extraneous material. The jargon that ACT puts into the science section is likely why many people become so overwhelmed by it. Indeed, they try to stress you out psychologically from the beginning of the test with all the jargon, unconventional graphs, and short time limit. You can overcome these factors easily by taking several subject tests, as they'll help you identify the material.
I also recommend that you organize the order that you do your passages. The general consensus is to do all of the data representation (5 question) first, then the research summaries (6 questions), and finally the conflicting viewpoints passage (7 questions). Most people believe that this is the most efficient order to do the paragraphs, and that it will leave you the most time for the longest passage - the conflicting viewpoints one. Personally, I do the passages in this order: physics, chemistry, then biology. (I'm terrible at certain biology passages though, so I'd prefer to not get stressed early on by one of those.) In my opinion, if you're aiming for a score in the 30's, then you'll finish all of the passages anyways, so the order isn't terribly critical. Just don't spend too long turning pages and always make sure to check the corresponding bubbles! (20-30 seconds is more than enough to notice that you should skip a passage.)
Also, if you do choose to do the questions without read the passage, then do the first question rule. If you don't know the first question (as it's often the easiest), then skip the passage until later.