Everything Braintree says above is true -- you should focus on official questions, but not on official explanations, and your outstanding Verbal skills should translate well to Quant if you approach that section in the right way. It really is a test of reasoning, and if you understand GMAT math concepts, you'll be able to use the same conceptual and logical abilities you're using in CR and SC to answer math questions. I'd almost always expect someone at your Verbal level to be able to score a Q47+ if they learn math the right way, so I think you should be able to improve your Q score a lot.
A few haphazard comments about issues that have come up in this thread:
• it's hard to improve on very high Verbal scores; there aren't any prep materials designed to help with the subtle questions you'll see when you're scoring in the V40 range. From the study materials you're using, the one recommendation I'd make is to study official GMAT CR and RC questions. LSAT questions can be good practice, but they're stylistically different from GMAT questions. Using official CR and RC questions (and reviewing any wrong SC/CR/RC answers to official questions to see if you can learn anything from them) is really the only thing I think you could do to try to raise your Verbal score further;
• the Quant section, especially at the Q40+ level, is really a test of conceptual understanding and reasoning. If you were only looking at well-known prep company material,
MGMAT and Veritas (when it existed) were the only companies that really even tried to approach the test that way. Most companies either teach the test as if it were a high school math test (and want you to spend dozens of hours memorizing tons of formulas and methods, which is not at all what the test is about) or they teach as if the GMAT were a test of 'strategy' (so teach things like backsolving and number picking, techniques that can be useful to Q25 level test takers, but which are provably useless for Q40+ level test takers). You're exactly right when you say it takes too much time to work backwards from answer choices; it's a low level approach that doesn't even work on most hard questions, and when it does it's slower than a direct approach. That said, you should sometimes glance at answer choices when you've made some progress on a solution, to see if an estimate or other shortcut might let you bypass an awkward calculation.
• since you only have three weeks, you won't have time to learn all of GMAT math in a more conceptual way, so you should focus on the things most likely to be frequently tested: ratios, percents and word problems, along with algebra (especially fractions, exponents, equations and inequalities) and perhaps some number theory. If you're studying official questions, you can learn a lot about a conceptual approach just by reading solutions on this forum from Quant experts who take that approach, e.g. me, Avi Gutman, and Karishma B. You might also refer to the excellent (and free) video solutions of every OG question by Dabral (gmatquantum). Tutoring is expensive, but a good tutor would also be able to help you learn a conceptual approach, though in only three weeks you wouldn't be able to cover nearly everything.
• as for whether you can omit subjects, the important thing to understand about adaptive testing is that it hurts your score a lot when you answer an easy question incorrectly, but it doesn't really hurt at all if you answer a very hard question incorrectly. So if your foundation in a subject is so weak that you might not even answer a 300-level question correctly, you'll be running a risk on every test: you might see a 300-level question on that subject, and need to guess, and unless that guess is lucky you might have a hard time scoring well. Ideally you'd know enough about every important subject that you can at least answer most easy and medium level questions. Coordinate geometry, for example, will be important on some tests and irrelevant on others, but it's tested often enough that you'd be running a very real risk if you knew nothing about it. But within the major topics there are niche areas (like circular permutations or inverse variation) that are so rarely tested that you'd do best to ignore them if you have very little time to prepare. Of course there's a slim chance you'll see those topics on a test, but the probability is much, much higher that you'll see percent increase or fraction arithmetic or divisibility questions, and you should be spending time learning things you'll very likely be tested on. You've studied from the OG+QR books, which will give you a good impression of how important each topic is, and I'd only spend time at this stage on things you've seen tested in more than one or two OG+QR questions.
Good luck!