Some people have a particular knack for "hearing" errors in a sentence and it is true that after a certain amount of practice and with a talent for such things it is possible to eliminate choices based on how they sound with a fair level of accuracy. This is the method that I used on the Sentence Correction the first time that I took the GMAT. I average 4 wrong on the sentence correction per verbal section compared to only one on the RC and CR combined (I mention this because you are in a similar - if more extreme position).
The last time I took the GMAT I scored a 51 on the verbal, meaning that I probably did not miss a question on the verbal including the 17 sentence correction questions. What is responsible for the turnaround? Easy, I stopped fighting with the test and started doing what the test makers intend for you to do.
Try to view everything on the GMAT as a test of your decision making abilities. For example, the quantitative section of the test is not actually designed because business schools want to make sure that you have coordinate geometry skills (for example), but rather just to give them a subject matter to test your decision making.
For sentence correction, you do need to know standard English grammar but you don't really have to have a lot of technical knowledge or terminology, you probably know more grammar than you realize. The key is to view each sentence correction as a series of decisions. Look at the answer choices to spot differences. Use these differences to guide you in eliminating incorrect answers. This is a completely different way of looking at sentence correction. You are not reading the entire sentence each time looking for the one that sounds best, but eliminating the incorrect answers based on definite choices like singular versus plural.
You can even try looking at the answer choices before you read the sentence (just to practice - not for test day) and work on identifying these differences in the answer choices. As you get better at spotting these you will be more confident in your sentence correction!
It takes a lot of skill to be able to read an answer choice and say if it is right or wrong. I certainly respect those, such as "inrockwetrust" who can eliminate based on a preliminary read through. However, if you are missing 11 on the sentence correction and 1 on critical reasoning I think that you will be better served to turn SC into CR by focusing on the differences in the answer choices. You should specifically look for the following five differences (excerpted from the VAMPIRES list of sentence correction errors that we study in the Veritas books and classes).
1. Number Agreement (including subject-verb, pronoun antecedent, etc.)
2. Misplaced Modifiers
3. Verb tense
4. Parallel elements/ Comparisons
5. Relative Clauses
Practicing look at answer choices to see where three choices do one thing and two do another. These differences will allow you to eliminate answer choices you have never even read!!! This is because you will be able to tell that, for example, the singular verb is correct and not the plural version. The time to focus on which answer choice sounds best is when you have already eliminated choices based on grammatical differences and you are down to two choices.
And one more thing, As your SC improves don't be surprised to face tougher CR and RC questions. This is because the verbal section adapts as a whole and so right now SC is holding back the difficulty of the entire section for you. Like the parking brake on when you are trying to drive. Fix your SC and the whole thing should be a fun, crazy ride.
Hope that helps!