I'm not so sure that plan will work. Often the questions ask about the tone of the passage, or the attitude of the author about something. You won't be able to answer those as accurately if you've only read the first and last paragraphs, and if you have to search through the passage for the tone, that's essentially reading the entire passage anyway.
With your strategy you could really get tripped up if the author offers some sort of acknowledgement of the weakness of his/her argument somewhere in the passage. If you haven't read the whole thing, get a tone/attitude question, then go back to the passage to look for the answer, you could find the author saying something negative about X and choose a negative attitude when really s/he was just acknowledging the other side's points.
Even aside from that situation, if you have a detail question and have to look through the entire passage for the detail, you'll essentially be skimming the entire passage every time you have to do that. I think it would be much faster to read the entire passage the first time and be able to focus your search on the area of the passage where you know the detail is located. There are also situations where a detail is referred to multiple times in one paragraph, but the text around the detail lets you know which one is most applicable. If all you're doing is looking for the detail, you could completely miss more applicable details and get the question wrong.
I adopted an approach pretty much opposite from the one you described, and that served me well. I found that once I gave myself more than the "recommended" time on the passage, I was able to fly through the questions because I was so comfortable with the passage. The slower I read, the more I remembered, and the less I needed to refer to the passage during the questions. I took the old MCAT where we only had 8 minutes per passage, and I would routinely give myself 4.5 minutes to read the passage.
Different things work for different people, so it's good that you're experimenting and you may well find success with your method. Give it a go recognizing its potential weaknesses, and be willing to adjust if necessary. Good luck!