Hi foxtrotvictor,
We can definitely help you! You are not alone in your struggle with this test. It is a very difficult and unusual test that most people find very challenging. I do have some questions for you about how you are studying that will help me and some of the other instructors help guide your studying. What prep course have you taken? What materials, other than the LSAC books, are you using? In particular, what helped you improve your accuracy on the LR and RC sections? Also, since you excluded AR from your range of 18-20 correct, how are you doing on that section?
You have already made progress in increasing your accuracy on LR and RC, so that indicates to me that you know what you are doing for a decent number of the questions and how to attack them, but you need to be faster. There are not really any shortcuts or tricks that are going to increase your speed on this test. The only way to go faster once you have the technique down is doing lots of practice. For example, lets say there are nine steps that you need to do to answer each question and you can do them accurately, but it takes you 3 minutes per question. To increase your speed, you are not going to skip any of those nine steps because that will just decrease your accuracy. You need to practice those steps over and over until you can do all nine faster.
You also mention that being timed feels unnatural, which is true for many students. Timed practice will certainly help you. Once you feel confident that you can answer questions correctly untimed, you need to start timing your practice. Taking timed practice tests will get you comfortable with the time element and it will hopefully not feel as unnatural to you.
Without knowing what you are working from at the moment, I would highly recommend getting the PowerScore Bibles, especially the Logic Games Bible and the Logical Reasoning Bible, to go along with full length practice tests. They will help you learn how to attack question types you are still struggling with and provide further clarification and practice on the types you are already improving on. Solidifying your understanding of the concepts and questions, combined with lots of practice should get you the increase you are wanting.
You have a great attitude about the test and are clearly willing to put in the necessary time to increase your score so I see no reason why you won't succeed. Since you have time and money is an understandable concern, I would suggest studying and practicing on your own with the Bibles and other materials you may already have and after you have worked through a decent amount of the material, consider hiring a tutor for the concepts you are still struggling with. That way you will get the one on one help that you prefer with the difficult material. Here is a link to some self study plans and recommended materials that may help guide you in creating a specific plan of attack:
http://students.powerscore.com/self-study/index.cfm
I'm sure some of my colleagues will chime in with some other great advice for you as well. I hope this helps.
Ladan