You are absolutely right to see some of those "most supported" questions as being quite unique relative to other LSAT questions -- the right answers are commonly not 100% justifiable. Along with Explain the Discrepancy, Most Support is the question type that consistently leaves me feeling the least satisfied in terms of finding a right answer that fits live a glove. Regardless, I still have 100% confidence that I'll get these questions correct -- if you don't mind, I'll take a bit of a roundabout way of explaining why --
First, can you think of the biggest structural difference between these two math questions?
1. What is 2 + 3?
2. Which of these is an odd number?
In the first case, the question stem completely determines the answer -- I know 2 + 3 is 5, I do the work, and I look for 5. I really spend no time thinking about the other answers.
In the second case, I'm looking for certain characteristics in the answer choices -- I know 3 has what I am looking for, but I also know that 2 and 4 do not. The accurate LSAT way to make this decision if your life depended on it would be to first eliminate the numbers that are not odd, then confirm (maybe by trying to divide by two) that the remaining answer is indeed odd.
It's important to remember that Most Support are far more like the second of those math problems than the first. The other important factor to think of is what I call "the test writer's burden." The test writer MUST come up with clear distinctions between the right answer and the four wrong answers -- that's his job.
As we discussed, when it comes to Most Support questions, right answers are commonly not slam-dunk provable. So, how do they clearly differentiate that right answer from the wrong ones?
By making the wrong ones slam-dunk bad. The nature of the question is such that the wrong answers are always very clearly wrong, and (just like in an orientation question for a logic game) it's much easier to see why wrong answers are wrong than to see why the right answer is right.
So, all this is just a long-winded way of saying that I really believe the elimination process is critical for solving these questions, and that has to do with the way the questions are designed. If I were asked to describe what right answers to these questions feel like, I would say "pretty reasonable." If I walk into the answer choices for a Most Support question with a mindset that I'm going to see which answer sounds "pretty reasonable," these questions are really hard -- a lot of answers seem pretty reasonable. If I walk in thinking "why don't these match the text," (and keep in mind that for the first round of eliminations I'm looking for significant, not subtle, differences in content or meaning) wrong answers jump out. Even for the hardest questions, after the elimination process, the vast majority of time I will have just one answer to really carefully evaluate and deem "reasonable."
HTH - please let me know if you have any follow up q's and good luck.